# What is Physical pendulum: Definition and 78 Discussions

A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.

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1. ### Compound physical pendulum - max velocity

Hi, I'm working on a simple benchmark problem for FEA. It's a pendulum initially positioned at an angle of ##45^{\circ}## and then subjected to gravity. I'm interested in the maximum velocity (when the pendulum is in the vertical position). So far, I've been using this formula: v=\omega \cdot...
2. ### Physical Pendulum - Theoretical equation

Initially I went from: T = 2π√(2L/3g) T = 2π/√(3g) * √(2L) To finally this equation: T = 2π/√(3g) * √(L) Where 2L becomes L as the 2 is lost. I am not fully sure if this is correct or how to properly get rid of the 2 in 2L.We must follow the rule of y = mx+c whereby y = T, m = the constant...
3. ### Moment of inertia of a double physical pendulum

I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below
4. ### How Does Pivot Point Location Affect the Time Period of a Physical Pendulum?

hello, i have some diffuculties with this problem, there's the point where the spring is attached to the rod and according to the equation of time period of physical pendulum , h represent the distance from the COM and the pivot point. here the pivot point is at the COM. and i know that it can't...
5. ### Forces that act on a physical pendulum

hello, i have a question about the forces that act on a rod at it's pivot point. the rod is free to rotate about the pivot point at the edge and it starts from rest parallel to the ground.the question is : when it reach to angle theta find the a] the angular velocity b] angular acceleration c]...
6. ### Equation Demonstration -- Comparing a pendulum's motion to an LC circuit

I've just learned about simple harmonic motion and I've been given the following examples: The physical pendulum (for small oscillations sin(theta)~theta), with the formula (1st pic), and the LC circuit, with the formula (2nd pic). If possible, I need the demonstration for these 2 formulas...
7. ### Period of a physical pendulum with a pivot at its center

Homework Statement The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order. Homework Equations T = 2π / ( I/mgh) I = Icm + mh2 Icm=(ML2/12) The Attempt at a Solution I have found the period for first...
8. ### Angular frequency of a physical pendulum

Homework Statement For calculating angular frequency of a physical pendulum, I consider its center of mass motion. The COM motion is a simple pendulum motion. Considering a coordinate system whose origin is the pivot point. Then, the COM is the length of the corresponding simple pendulum. Is...
9. ### Simple Harmonic Motion/Period of a Physical Pendulum

I'm studying the motion of a physical pendulum, could someone help me make the final step in figuring out how to find the period so I can make predictions before carrying out a practical? Basically I have a meter rule with holes drilled along the length and will be pivoting it at various points...
10. ### Physical pendulum with no fixed pole

1. Homework Statement The violet sleeve has mass M and is free to move horizontally without friction. The green rod has mass 2M and length L and can rotate around a pivot on the sleeve without friction. At t=0, the rod is in vertical position and is rotating with angular velocity w. What are...
11. ### Physical Pendulum - Rod - Period and Distance From Center of Mass

Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...
12. ### Maximum Kinetic Energy from a Physical Pendulum

Homework Statement Determine the maximum kinetic energy of a uniform rod of mass 0.5Kg and length 0.75 that has an angular displacement of 5 degrees. Homework Equations y = rsin (x) where x is the angular displacement The Attempt at a Solution Using conservation of energy ETotal = EMech +...
13. ### Potential energy in a physical pendulum

Hey PF! 1. Homework Statement If I have a pendulum; a vertically hanging rod with (length ##L## and mass ##m##) which can rotate freely about a point ##p## on the upper edge of the rod. Now I fire a bullet (also with mass ##m##) into it (strictly horizontal on the lower end of the rod). I...
14. ### Angular velocity for a physical pendulum

Homework Statement I have a physical pendulum made of a leg which mass is ignored, with a length of 1m, two objects of mass are placed on the bottom and the top of the leg, the first with a mass of m1= m1, and the second with a mass of m2= 3m1, both are L/2 away from the pivot point. It's...
15. ### Physical Pendulum Question (Mass on a Grandfather Clock)

Homework Statement You are at a furniture store and notice that a grandfather clock has its time regulated by a physical pendulum that consists of a rod with a movable weight on it. When the weight is moved downward, the pendulum slows donw; when it is moved upward, the pendulum swings faster...
16. ### Compare Pendulum Angular Frequencies for Cases A & B

Homework Statement A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (<L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached : Case A: The disc is not free to rotate about its centre of mass, the...
17. ### Time period of a pendulum made of two disks

Homework Statement Problem statement - [/B] Klepner and Kolenkow 6.15 : A pendulum is made of two disks each of mass M and radius R separated by a massless rod. One of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centres are a distance l...
18. ### Dimensional analysis of a physical pendulum

Hi! Sorry if this is the wrong section to post this: I am doing a laboration on physical pendulums and I have a bit of trouble making sense of it all and I am in need of some guidance. When I do the analysis I get the standard mathematical pendulum. [T]=[m]^a*[l]^b*[g]^c, where a = 0, b = -c...
19. ### Physical Pendulum Formula Derivation

Homework Statement A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x. The aim is to derive a...
20. ### Physical pendulum in phase space

Hi, I found out this paper http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendulum.pdf with this animation http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendula.html At first there is written there, that the area of possible states in some range...
21. ### Physical pendulum thin rods problem

Homework Statement Two identical thin rods, each with mass m and length L, are joined at right angles to form an L shaped object. This object is balanced on top of a sharp edge. If the L shaped object is deflected slightly, it oscillates. Find the frequency of oscillation. Here is a picture...
22. ### Lab Project - build a physical pendulum with the smallest period

Hi, I'm a student working with my group to create a lab for our final lab project. Me and my teammates are stuck on how we should begin to set up the project. I attached 4 photos, one of the pendulum setup, one of the model of our pendulum setup, and two others of the lab sheet guide. The...
23. ### The physical pendulum - mass calculations

When analysing the forces/energy transfers acting on a physical pendulum (albeit with a larger mass on the end, such as a grandfather clock...with a thick rod?) is it absolutely necessary to know the mass of the 'arm' (separate from the bob, as such)? Also, can the mass of the arm be calculated...
24. ### Time period of oscillation of a physical pendulum and spinning disk

Homework Statement Find the period of a pendulum consisting of a disk of mass M and radius R fixed to the end of the rod of length l and mass m. How does the period change if the disk is mounted to the rod by a friction less bearing so that it is perfectly free to spin? The centre of the...
25. ### Moment of inertia physical pendulum

Homework Statement I have a physical pendulum that is rotating about an fixed axis. The period is: T=2\pi \sqrt{\frac{I}{mgd}} I = moment of inertia d = distance between the center of mass and the axis. The problem is: If you add a mass in the end of the pendulum. The period is going...
26. ### Period of a Physical Pendulum: Finding T for a Uniform Disk

Homework Statement A uniform metal disk (M = 9.81 kg, R = 8.99 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations. Homework Equations I (uniform disk, with axis through center of mass) = (1/2)MR^2 T = 2π√(I/mgd)...
27. ### Inverted physical pendulum, time taken to hit ground.

I'm currently preparing for a classical prelim and am concerned that this problem may not be correct. I'm second guessing myself due to the hint given in the problem, which I did not use. Any help is more than appreciated. A picture of the pendulum is included. Homework Statement A...
28. ### T = 2π√I/g but I am getting the wrong answer.Pendulum Periods: A & B (L, m)

Homework Statement Two pendulums have the same dimensions (length ) L and total mass (m). Pendulum A is a very small ball swinging at the end of a uniform massless bar. In pendulum B , half the mass is in the ball and half is in the uniform bar. A. Find the period of pendulum A for small...
29. ### The physical pendulum - distance, period, and angular frequency

Homework Statement The physical pendulum shown on your paper is a 27.0 kg wedge of a circular disk of uniform density with radius, R=1.87 m and opening angle β=0.847 radians. The pivot point of the pendulum can be moved along the center line of the wedge as shown on your paper...
30. ### Physical pendulum made of a uniform disk

Homework Statement A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum? Homework Equations The Attempt at a Solution
31. ### Solving for Period of a Physical Pendulum - Homework Help

Homework Statement A very light rigid rod with a length of 0.516 m extends straight out from one end of a meter stick. The combination is suspended from a pivot at the upper end of the rod as shown in the following figure. The combination is then pulled out by a small angle and released. a)...
32. ### Mechanical Energy of a Physical Pendulum

http://img196.imageshack.us/i/unledup.png/ So we have a physical pendulum. It has a mass of m=200 g and radius 10 cm. It's suspended from point O at a distance h=8 cm. from center C. It is displaced 0.1 rad and released from rest at t=0. I'm struggling to find the mechanical energy of this...
33. ### Nonlinear graph in the Physical Pendulum

We did an experiment using the physical pendulum to measure gravitational acceleration g. A graph is shown in this link: http://i593.photobucket.com/albums/tt20/omicgavp/measuringggraph.jpg" A nonlinear (possibly chaotic) trend can be seen in our graph even though we assumed small-amplitude...
34. ### Introductory Physical Pendulum Problem

Homework Statement A pendulum is constructed using a thin rod (m1 = 2.0 kg, L = 1.0m) and a uniform sphere (m2 = 1.0 kg, R = 0.50 m). The period in "s" for small oscillations is: a) 1.5 b) 1.7 c) 2.0 d) 2.2 e) 2.5 Homework Equations T = 2pi *sqrt(I/mgd) The Attempt at a...
35. ### Shortest period for a physical pendulum

Homework Statement meter stick pivoted at point a from its center and swings as a physical pendulum. At which values of a gives you the shortest period of oscillation...1m, .2m, .3m, .4m. .5m Homework Equations T = 2pi*Sqrt(I/mgh) The Attempt at a Solution the shortest a should...
36. ### How Do You Calculate the Moment of Inertia for a Compound Physical Pendulum?

1. Homework Statement Ok So here's my question. The physical Pendulum consists of a thin rod of mass m = 100 g and length 80 cm, and a spherical bob of mass M = 500 g and radius R = 25 cm. There a pivot P at the top of the rod. (Sorry, I don't have a picture >.<) a) It asks for the center of...
37. ### Physical Pendulum Question for Moment of Inertia

Homework Statement Ok So here's my question. The physical Pendulum consists of a thin rod of mass m = 100 g and length 80 cm, and a spherical bob of mass M = 500 g and radius R = 25 cm. There a pivot P at the top of the rod. (Sorry, I don't have a picture >.<) a) It asks for the center of...
38. ### Physical Pendulum and moment of inertia

A physics student measures the period of a physical pendulum about one pivot point to be T. Then he finds another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Can he find the acceleration due to gravity, g...
39. ### Solving Physical Pendulum Homework Equation

Homework Statement http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html#c2 i'm trying to prove to be Homework Equations Letting d = Lcm now we already know \partial^2\vartheta/\partial t^2 = \alpha = mgdT\vartheta / I I tried integrating the whole equation wrt dt so...
40. ### Physical pendulum: frequency of rotated square

1. A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper corner. If it is rotated slightly and then released, at what frequency will it swing back and forth? Homework Equations...
41. ### Measuring g with Physical Pendulum Time Period (T)

Homework Statement Ok worked out the time period of a physical pendulum (T) to be (in terms of constant a, and variable length x): T^2 = 4pi (1/2a^2 + x^2)/(gx) Now asked how i could use a measurement of T(x) to measure g. Homework Equations The Attempt at a Solution I...
42. ### Walking legs as physical pendulum oscillations

Homework Statement The typical walking speed of a person walking at a relaxed pace can be estimated by modelling their legs as a physical pendulum. Assume that the length of a person's leg is L and it pivots about the hip and the leg is tapered (more mass towards the hip and less towards the...
43. ### Kinematics of Inverted Physical Pendulum

Homework Statement A stick of mass M, length L, stands upright on a table, pivoted to the table. What is the angular velocity as it hits the table? Homework Equations ang. accel = (3g/2L)cos theta w = (3g/2L) integral cos theta dt The Attempt at a Solution theta (t) = ...
44. ### What is the Angular Velocity of a Falling Physical Pendulum?

Homework Statement A stick of mass M, length L is standing upright on a table, pivoted at the bottom. What is its angular velocity as it hits the table? Homework Equations ang. accel = (3g/2L)cos theta (theta is zero with stick laying on table) The Attempt at a Solution...
45. ### What is the final angular velocity of a falling physical pendulum?

All -- With a meter stick standing straight up and pivoted at the *bottom*, what is the final angular velocity as it hits the table? I've found plenty of standard stuff on physical pendulums (meter stick pendulum), where I = 1/12 MR^2, period, etc, but I can't find velocity info...
46. ### Calculating Moment of Inertia for a Physical Pendulum

Hi, Would appreciate any help anyone has for me. I am building a physical pendulum of sort, which consists of a hollow cylinder, which I am going to fill with sand. I am going to let the sand flow out of the pendulum and investigate the change in period with changing mass. I also am...
47. ### Physical pendulum wrench oscillations

Question Details: A 1.44 kg monkey wrench is pivoted at one end and allowed to swing as a physical pendulum. The period of its motion is 0.860 s, and the pivot is 0.290 m from the center of mass of the wrench. (a) What is the moment of inertia of the wrench? 0.0767 kgm2 If the wrench is...
48. ### What Is the Period of Oscillation for a Hoop Suspended by Its Perimeter?

Homework Statement a hoop of radius R=.18m and mass=.44kg is suspended by a point on its perimeter. If the hoop is allowed to oscillate side to side, what is the period of oscillation? Homework Equations I=MR^2 plus an offset? MR^2 so I=2(MR^2)? PE=1/2kx^2 w=(2pi)/T KErot=1/2Iw^2...
49. ### How Is the Optimal Pivot Distance Calculated for a Uniform Disk Pendulum?

Homework Statement A uniform disk of radius R = 1.40 m and a 6.0 kg mass has a small hole a distance d from the disk's center that serves as a pivot point. What should be the distance d so that this physical pendulum will have the shortest possible period? Homework Equations T =...
50. ### How Does Mass Distribution Affect the Frequency of a Physical Pendulum?

Homework Statement A long, straight, and massless rod pivots about one end in a vertical plane. In configuration I, two small identical masses are attached to the free end; in configuration II, one mass is moved to the center of the rod. What is the ratio of the frequency of small oscillations...