The units for the torsion constant are [\(\kappa\)] = N m = (kg m/s2)m = kg m2/s2 and the units for the moment of inertial are [I] = kg m2, which show that the unit for the period is the second. /F7 24 0 R /F6 21 0 R Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia I = \(\int\)r2 dm times the angular acceleration \(\alpha\), where \(\alpha = \frac{d^{2} \theta}{dt^{2}}: \[I \alpha = \tau_{net} = L (-mg) \sin \theta \ldotp\]. Even simple . We first need to find the moment of inertia of the beam. See Full PDF /F9 30 0 R Non-profit, educational or personal use tips the balance in favour of fair use. Like the force constant of the system of a block and a spring, the larger the torsion constant, the shorter the period. Legal. 4 2/T 2. This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. We are asked to find g given the period T and the length L of a pendulum. Newtonian MechanicsFluid MechanicsOscillations and WavesElectricity and MagnetismLight and OpticsQuantum Physics and RelativityThermal PhysicsCondensed MatterAstronomy and AstrophysicsGeophysicsChemical Behavior of MatterMathematical Topics, Size: from small [S] (benchtop) to extra large [XL] (most of the hall)Setup Time: <10 min [t], 10-15 min [t+], >15 min [t++]/span>Rating: from good [] to wow! For small displacements, a pendulum is a simple harmonic oscillator. A 3/4" square 18" long 4 steel bar is supplied for this purpose. Consider a coffee mug hanging on a hook in the pantry. The distance between two knife edges can be measured with great precision (0.05cm is easy). The period, \(T\), of a pendulum of length \(L\) undergoing simple harmonic motion is given by: \[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]. Enter the email address you signed up with and we'll email you a reset link. >> In this experiment, we measured \(g\) by measuring the period of a pendulum of a known length. A graph is drawn between the distance from the CG along the X-axis and the corresponding time period along the y-axis.Playlist for physics practicals in hindi.https://youtube.com/playlist?list=PLE9-jDkK-HyofhbEubFx7395dCTddAWnjPlease subscribe for more videos every month.YouTube- https://youtube.com/channel/UCtLoOPehJRznlRR1Bc6l5zwFacebook- https://www.facebook.com/TheRohitGuptaFBPage/Instagram- https://www.instagram.com/the_rohit_gupta_instagm/Twitter- https://twitter.com/RohitGuptaTweet?t=1h2xrr0pPFSfZ52dna9DPA\u0026s=09#bar #pendulum #experiment #barpendulum #gravity #physicslab #accelerationduetogravityusingbarpendulum #EngineeringPhysicsCopyright Disclaimer under Section 107 of the copyright act 1976, allowance is made for fair use for purposes such as criticism, comment, news reporting, scholarship, and research. Assuming the oscillations have a frequency of 0.50 Hz, design a pendulum that consists of a long beam, of constant density, with a mass of 100 metric tons and a pivot point at one end of the beam. This will help us to run this website. The compound pendulum is apt at addressing these shortcomings and present more accurate results. We adjusted the knots so that the length of the pendulum was \(1.0000\pm0.0005\text{m}\). Several companies have developed physical pendulums that are placed on the top of the skyscrapers. Find the positions before and mark them on the rod.To determine the period, measure the total time of 100 swings of the pendulum. [] or not rated [], Copyright 2023 The President and Fellows of Harvard College, Harvard Natural Sciences Lecture Demonstrations, Newton's Second Law, Gravity and Friction Forces, Simple Harmonic (and non-harmonic) Motion. >> Measurement of acceleration due to gravity (g) by a compound pendulum Aim: (i) To determine the acceleration due to gravity (g) by means of a compound pendulum. For example, it's hard to estimate where exactly the center of the mass is. (ii) To determine radius of gyration about an axis through the center of gravity for the compound pendulum. Use the moment of inertia to solve for the length L: $$\begin{split} T & = 2 \pi \sqrt{\frac{I}{mgL}} = 2 \pi \sqrt{\frac{\frac{1}{3} ML^{2}}{MgL}} = 2 \pi \sqrt{\frac{L}{3g}}; \\ L & = 3g \left(\dfrac{T}{2 \pi}\right)^{2} = 3 (9.8\; m/s^{2}) \left(\dfrac{2\; s}{2 \pi}\right)^{2} = 2.98\; m \ldotp \end{split}$$, This length L is from the center of mass to the axis of rotation, which is half the length of the pendulum. Your email address will not be published. If this experiment could be redone, measuring \(10\) oscillations of the pendulum, rather than \(20\) oscillations, could provide a more precise value of \(g\). To determine the radius of gyration about an axis through the centre of gravity for the compound pendulum. But note that for small angles (less than 15), sin \(\theta\) and \(\theta\) differ by less than 1%, so we can use the small angle approximation sin \(\theta\) \(\theta\). . As the skyscraper sways to the right, the pendulum swings to the left, reducing the sway. You can download the paper by clicking the button above. The minus sign shows that the restoring torque acts in the opposite direction to increasing angular displacement. Find more Mechanics Practical Files on this Link https://alllabexperiments.com/phy_pract_files/mech/, Watch this Experiment on YouTube https://www.youtube.com/watch?v=RVDTgyj3wfw, Watch the most important viva questions on Bar Pendulum https://www.youtube.com/watch?v=7vUer4JwC5w&t=3s, Please support us by donating, Have a good day, Finally found the solution of all my problems,the best website for copying lab experiments.thanks for help, Your email address will not be published. Performing the simulation: Suspend the pendulum in the first hole by choosing the length 5 cm on the length slider. Theory The period of a pendulum (T) is related to the length of the string of the pendulum (L) by the equation: T = 2 (L/g) Equipment/apparatus diagram 1 size of swing . Theory. The uncertainty is given by half of the smallest division of the ruler that we used. The magnitude of the torque is equal to the length of the radius arm times the tangential component of the force applied, |\(\tau\)| = rFsin\(\theta\). [Caution: Students are suggested to consult Lab instructors & teachers before proceeding to avoid any kind of hazard.]. The Italian scientist Galileo first noted (c. 1583) the constancy of a pendulum's period by comparing the movement of a swinging lamp in a Pisa cathedral with his pulse rate. We thus expect to measure one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% relative uncertainty on the period). Objective The following data for each trial and corresponding value of \(g\) are shown in the table below. To determine g, the acceleration of gravity at a particular location.. Kater's pendulum, stopwatch, meter scale and knife edges. Thus, by measuring the period of a pendulum as well as its length, we can determine the value of \(g\): \[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\] We assumed that the frequency and period of the pendulum depend on the length of the pendulum string, rather than the angle from which it was dropped. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. /MediaBox [0 0 612 792] The restoring torque is supplied by the shearing of the string or wire. Using the small angle approximation and rearranging: \[\begin{split} I \alpha & = -L (mg) \theta; \\ I \frac{d^{2} \theta}{dt^{2}} & = -L (mg) \theta; \\ \frac{d^{2} \theta}{dt^{2}} & = - \left(\dfrac{mgL}{I}\right) \theta \ldotp \end{split}\], Once again, the equation says that the second time derivative of the position (in this case, the angle) equals minus a constant \(\left( \dfrac{mgL}{I}\right)\) times the position. To determine the acceleration due to gravity 'g' by using bar pendulumBar PendulumBar Pendulum ExperimentCompound Pendulum ExperimentAcceleration due to gravityAcceleration due to gravity using bar pendulumAcceleration due to gravity by using bar pendulumAcceleration due to gravity by using bar pendulum experimentPhysics Experimentbsc Physics Experimentbsc 1st yearbsc 1st year physicsbsc 1st semesterbsc 1st semester physicsWhat is the formula of acceleration due to gravity by bar pendulum?How do we measure g using bar pendulum method?#BarPendulum#CompoundPendulum#Accelerationduetogravityusingbarpendulum#BarPendulumExperiment#CompoundPendulumExperiment#Accelerationduetogravity#PhysicsExperiment#bscPhysicsExperiment#bsc1styear#bsc1styearphysics#bsc1stsemester#bsc1stsemesterphysics#bsc_1st_semester#bsc_1st_semester_physics#PhysicsAffairs This method for determining g can be very accurate, which is why length and period are given to five digits in this example. The locations are; Rafin Tambari, Garin Arab, College of Education Azare and Township Stadium Azare. 1 The reversible pendulum was first used to measure g by Captain Henry Kater: H. Kater, Philos Trans Roy Soc London 108, 33 (1818).2 B. Crummett, The Physics Teacher 28, 291 (1990).3 Sargent-Welch Scientific model 8124 It's length was measured by the machine shop that made it and has the value 17.9265" stamped on its side. II Solucionario, The LTP Experiment on LISA Pathfinder: Operational Definition of TT Gauge in Space, Solucionario de Fsica Universitaria I, 12a ed, Fsica Para Ingenieria y Ciencias Ohanian 3ed Solucionario. Save my name, email, and website in this browser for the next time I comment. Using a simple pendulum, the value of g can be determined by measuring the length L and the period T. The value of T can be obtained with considerable precision by simply timing a large number of swings, but comparable precision in the length of the pendulum is not so easy. Like the simple pendulum, consider only small angles so that sin \(\theta\) \(\theta\). This experiment uses a uniform metallic bar with holes/slots cut down the middle at regular intervals. To determine the acceleration due to gravity 'g' by using bar pendulumBar PendulumBar Pendulum ExperimentCompound Pendulum ExperimentAcceleration due to grav. There are many way of measuring this gravity acceleration, but the experiment of compound pendulum is the easiest and effective among them. In this video, Bar Pendulum Experiment is explained with calculatio. Object: To determine the acceleration due to gravity (g) by means of a compound pendulum. Useful for B.Sc., B.Tech Students. A typical value would be 2' 15.36" 0.10" (reaction time) giving T = 1.3536 sec, with an uncertainty of 1 msec (timing multiple periods lessens the effect reaction time will have on the uncertainty of T). The time period is determined by fixing the knife-edge in each hole. An engineer builds two simple pendulums. %PDF-1.5 The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty. Set up the apparatus as shown in the diagram: Measure the effective length of the pendulum from the top of the string to the center of the mass bob. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. The angle \(\theta\) describes the position of the pendulum. In the experiment the acceleration due to gravity was measured using the rigid pendulum method. Surprisingly, the size of the swing does not have much effect on the time per swing . The minus sign indicates the torque acts in the opposite direction of the angular displacement: \[\begin{split} \tau & = -L (mg \sin \theta); \\ I \alpha & = -L (mg \sin \theta); \\ I \frac{d^{2} \theta}{dt^{2}} & = -L (mg \sin \theta); \\ mL^{2} \frac{d^{2} \theta}{dt^{2}} & = -L (mg \sin \theta); \\ \frac{d^{2} \theta}{dt^{2}} & = - \frac{g}{L} \sin \theta \ldotp \end{split}\]. Here, the length L of the radius arm is the distance between the point of rotation and the CM. Fair use is a use permitted by copyright statute that might otherwise be infringing. /Parent 2 0 R We repeated this measurement five times. /F11 36 0 R The period, T, of a pendulum of length L undergoing simple harmonic motion is given by: T = 2 L g We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. This removes the reaction time uncertainty at the expense of adding a black-box complication to an otherwise simple experiment. % Manage Settings The results showed that the value of acceleration due to gravity "g" is not constant; it varies from place to place. /Length 5315 (adsbygoogle = window.adsbygoogle || []).push({});
. Taking the counterclockwise direction to be positive, the component of the gravitational force that acts tangent to the motion is mg sin \(\theta\). Even simple pendulum clocks can be finely adjusted and remain accurate. (PDF) To Determine The Value of g Acceleration due to gravity by means of a compound pendulum Home Acceleration To Determine The Value of g Acceleration due to gravity by. endobj stream iron rod, as rigidity is important. In this experiment the value of g, acceleration due gravity by means of compound pendulum is obtained and it is 988.384 cm per sec 2 with an error of 0.752%. The length of the pendulum has a large effect on the time for a complete swing. Kater's pendulum, shown in Fig. Read more here. Aim . By adding a second knife-edge pivot and two adjustable masses to the physical pendulum described in the Physical Pendulumdemo, the value of g can be determined to 0.2% precision. Pendulums are in common usage. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. The bar can be hung from any one of these holes allowing us to change the location of the pivot. Aim (determine a value for g using pendulum motion) To perform a first-hand investigation using simple pendulum motion to determine a value of acceleration due to the Earth's gravity (g). What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s? Legal. Sorry, preview is currently unavailable. In the experiment, the bar was pivoted at a distanice of Sem from the centre of gravity. A physical pendulum is any object whose oscillations are similar to those of the simple pendulum, but cannot be modeled as a point mass on a string, and the mass distribution must be included into the equation of motion. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. A digital wristwatch or large analog timer 3 is used to verify the period. % This is consistent with the fact that our measured periods are systematically higher. 1 Oxford St Cambridge MA 02138 Science Center B-08A (617) 495-5824. Thus you get the value of g in your lab setup. In this experiment the value of g, acceleration due gravity by means of compound pendulum is obtained and it is 988.384 cm per sec 2 with an error of 0.752%. An example of data being processed may be a unique identifier stored in a cookie. For the precision of the approximation sin \(\theta\) \(\theta\) to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about 0.5. We built the pendulum with a length \(L=1.0000\pm 0.0005\text{m}\) that was measured with a ruler with \(1\text{mm}\) graduations (thus a negligible uncertainty in \(L\)). This page titled 15.5: Pendulums is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Required fields are marked *. Start with the equation from above Square both sides to get Multiply both sides by g Divide both sides by T 2 This is the equation we need to make our calculation. In the experiment the acceleration due to gravity was measured using the rigid pendulum method. We suspect that by using \(20\) oscillations, the pendulum slowed down due to friction, and this resulted in a deviation from simple harmonic motion. Apparatus used: Bar pendulum, stop watch and meter scale. A compound pendulum (also known as a physical pendulum) consists of a rigid body oscillating about a pivot. Grandfather clocks use a pendulum to keep time and a pendulum can be used to measure the acceleration due to gravity. All of our measured values were systematically lower than expected, as our measured periods were all systematically higher than the \(2.0\text{s}\) that we expected from our prediction. The minus sign is the result of the restoring force acting in the opposite direction of the increasing angle. /F2 9 0 R 1 Objectives: The main objective of this experiment is to determine the acceleration due to gravity, g by observing the time period of an oscillating compound pendulum. We constructed the pendulum by attaching a inextensible string to a stand on one end and to a mass on the other end. The solution to this differential equation involves advanced calculus, and is beyond the scope of this text. A physical pendulum with two adjustable knife edges for an accurate determination of "g". This page titled 27.8: Sample lab report (Measuring g using a pendulum) is shared under a CC BY-SA license and was authored, remixed, and/or curated by Howard Martin revised by Alan Ng. Release the bob. To perform a first-hand investigation using simple pendulum motion to determine a value of acceleration due to the Earthsgravity (g). Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was measured over \(5\) trials. What It Shows An important application of the pendulum is the determination of the value of the acceleration due to gravity. Pendulum 1 has a bob with a mass of 10 kg. <>stream Continue with Recommended Cookies, if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[728,90],'physicsteacher_in-box-3','ezslot_8',647,'0','0'])};__ez_fad_position('div-gpt-ad-physicsteacher_in-box-3-0');This post is on Physics Lab work for performing a first-hand investigation to determine a value of acceleration due to gravity (g) using pendulum motion. !Yh_HxT302v$l[qmbVt f;{{vrz/de>YqIl>;>_a2>&%dbgFE(4mw. /Contents 4 0 R We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. The solution is, \[\theta (t) = \Theta \cos (\omega t + \phi),\], where \(\Theta\) is the maximum angular displacement. This experiment is discussed extensively in order to provide an example of how students should approach experiments and how experimental data should be processed. /Font << Our final measured value of \(g\) is \((7.65\pm 0.378)\text{m/s}^{2}\). The vertical pendulum, such as that developed by ONERA, 12 uses gravity to generate a restoring torque; therefore, it has a fast response to thrust due to the larger stiffness. A pendulum exhibits simple harmonic motion (SHM), which allowed us to measure the gravitational constant by measuring the period of the pendulum. In difference location that I used to and Garin Arab has the lowest value of acceleration due to gravity which is (9.73m/s 2). The period of a simple pendulum depends on its length and the acceleration due to gravity. We have described a simple pendulum as a point mass and a string. /Resources << Determination of Acceleration Due To Gravity in Katagum Local Government Area of Bauchi State, Solved Problems in Classical Physics An Exercise Book, 1000-Solved-Problems-in-Classical-Physics-An-Exercise-Book.pdf, Fisica Universitaria Sears Zemansky 13va edicion Solucionario 20190704 5175 1ci01va, FIRST YEAR PHYSICS LABORATORY (P141) MANUAL LIST OF EXPERIMENTS 2015-16, Classical Mechanics: a Critical Introduction, SOLUTION MANUAL marion classical dynamics, Soluo Marion, Thornton Dinmica Clssica de Partculas e Sistemas, Waves and Oscillations 2nd Ed by R. N. Chaudhuri.pdf, Lecture Notes on Physical Geodesy UPC 2011, Pratical physics by dr giasuddin ahmed and md shahabuddin www euelibrary com, Practical physics by dr giasuddin ahmad and md shahabudin, Practical Physics for Degree Students - Gias Uddin and Shahabuddin, Classical Mechanics An introductory course, Fsica Universitaria Vol. We also worry that we were not able to accurately measure the angle from which the pendulum was released, as we did not use a protractor. Theory A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. The formula then gives g = 9.8110.015 m/s2. The corresponding value of \(g\) for each of these trials was calculated. To overcome this difficulty we can turn a physical pendulum into a so-called reversible (Kater's) 1 pendulum. /F4 15 0 R ], ICSE, CBSE class 9 physics problems from Simple Pendulum chapter with solution, How to Determine g in laboratory | Value of acceleration due to gravity -, Simple Harmonic Motion of a Simple Pendulum, velocity of the pendulum bob at the equilibrium position, Transfers between kinetic & potential energy in a simple pendulum, Numerical problem worksheet based on the time period of pendulum, Acceleration, velocity, and displacement of projectile at different points of its trajectory, Satellite & Circular Motion & understanding of Geostationary Satellite. As for the simple pendulum, the restoring force of the physical pendulum is the force of gravity. We can then use the equation for the period of a physical pendulum to find the length. Use a stopwatch to record the time for 10 complete oscillations. /F1 6 0 R The force providing the restoring torque is the component of the weight of the pendulum bob that acts along the arc length. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds toupgrade your browser. With the simple pendulum, the force of gravity acts on the center of the pendulum bob. /F8 27 0 R Learning Objectives State the forces that act on a simple pendulum Determine the angular frequency, frequency, and period of a simple pendulum in terms of the length of the pendulum and the acceleration due to gravity Define the period for a physical pendulum Define the period for a torsional pendulum Pendulums are in common usage. In the case of the physical pendulum, the force of gravity acts on the center of mass (CM) of an object. The Kater's pendulum used in the instructional laboratories is diagramed below and its adjustments are described in the Setting It Up section. The rod is displaced 10 from the equilibrium position and released from rest. A rod has a length of l = 0.30 m and a mass of 4.00 kg. Recall that the torque is equal to \(\vec{\tau} = \vec{r} \times \vec{F}\). /Filter /FlateDecode In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\). A . We can solve T = 2\(\pi\)L g for g, assuming only that the angle of deflection is less than 15. In an experiment to determine the acceleration due to gravity, s, using a compound pendulum, measurements in the table below were obtained. A solid body was mounted upon a horizontal axis so as to vibrate under the force of gravity in a . x^][s9v~#2[7U]fLdIP/H*78 @%5e`hg+RjVou+Y+lN;Zmmwg/ z+qV'zePtC};niO(lY_on}f?ASwouQf4|2o}@[@ sqF&. Accessibility StatementFor more information contact us atinfo@libretexts.org. The experiment was conducted in a laboratory indoors. 27: Guidelines for lab related activities, Book: Introductory Physics - Building Models to Describe Our World (Martin et al. Best on the results findings, it showed that the Rafin Tambari has the highest value of acceleration due to gravity which is (10.2 m/s 2). 1, is a physical pendulum composed of a metal rod 1.20 m in length, upon which are mounted a sliding metal weight W 1, a sliding wooden weight W 2, a small sliding metal cylinder w, and two sliding knife . If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out. We are asked to find the length of the physical pendulum with a known mass. We are asked to find the torsion constant of the string. Often the reduced pendulum length cannot be determined with the desired precision if the precise determination of the moment of inertia or of the center of gravity are difficult. The mass, string and stand were attached together with knots. 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\newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Example \(\PageIndex{1}\): Measuring Acceleration due to Gravity by the Period of a Pendulum, Example \(\PageIndex{2}\): Reducing the Swaying of a Skyscraper, Example \(\PageIndex{3}\): Measuring the Torsion Constant of a String, 15.4: Comparing Simple Harmonic Motion and Circular Motion, source@https://openstax.org/details/books/university-physics-volume-1, State the forces that act on a simple pendulum, Determine the angular frequency, frequency, and period of a simple pendulum in terms of the length of the pendulum and the acceleration due to gravity, Define the period for a physical pendulum, Define the period for a torsional pendulum, Square T = 2\(\pi \sqrt{\frac{L}{g}}\) and solve for g: $$g = 4 \pi^{2} \frac{L}{T^{2}} ldotp$$, Substitute known values into the new equation: $$g = 4 \pi^{2} \frac{0.75000\; m}{(1.7357\; s)^{2}} \ldotp$$, Calculate to find g: $$g = 9.8281\; m/s^{2} \ldotp$$, Use the parallel axis theorem to find the moment of inertia about the point of rotation: $$I = I_{CM} + \frac{L^{2}}{4} M = \frac{1}{12} ML^{2} + \frac{1}{4} ML^{2} = \frac{1}{3} ML^{2} \ldotp$$, The period of a physical pendulum has a period of T = 2\(\pi \sqrt{\frac{I}{mgL}}\).

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