What is Pendulum: Definition and 999 Discussions

A pendulum is a weight suspended from a pivot so that it can swing freely. 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 back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geo-physical surveys, and even as a standard of length. The word "pendulum" is new Latin, from the Latin pendulus, meaning 'hanging'.

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  1. Hak

    Foucault Pendulum at the North Pole

    Consider a pendulum swinging at the North Pole in an inertial frame of reference xyz with the x and y axes in the plane tangent to the pole and the suspension placed at elevation z = l. There is no induction \mathbf{B} and in the chosen system the plane of oscillation xz of the pendulum is...
  2. FEAnalyst

    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...
  3. J

    B Why don't two double pendulum apparatus follow the same paths? / Chaos

    All double pendulum have same inital position, start from same height at same time, this softwear must have some equations from which calculate their path, so if both use same eqution and same inital position, why they have different paths(this is mathematicaly impossible)? One question about...
  4. S

    Pendulum SHO but with extra downward acceleration of the pivot

    Hey guys, Can someone help me understand how to understand this problem intuitively please? How I understand is that I need to look the acceleration relative to the lift as if it were f.e. on another planet with a different acceleration. this gives me a = g - 5. But then again if I didn't look...
  5. bob012345

    I Effect of Nearby Mountain on an Ideal Pendulum

    Suppose there is a very large mountain adjacent to a pendulum such that there is a horizontal component gravitational force of ##10^{-5}g## acting on the otherwise ideal pendulum. How would one use a perturbation to add that effect to first order? My initial thought would be to figure an angle...
  6. wrobel

    I A pendulum with viscous friction

    Consider the standard pendulum with a weightless rod of length b and a mass point m and mg is applied. In the hinge there is a torque of viscous friction which is proportional ##\omega^2##. Now release the pendulum from the horizontal position. What biggest height does the point m attain after...
  7. Q

    Physics IA: Distance B/w Pendulum & Alum. Block, Finding Damping Coefficient

    TL;DR Summary: I am doing an experiment for my Physics IA and don't know the theory behind it I am working on a Physics experiment for my school where I vary the distance between a simple pendulum and an aluminium block, and get the damping coefficient for each distance. Below are the images...
  8. D

    I Relevant/irrelevant clocks for experimental tests of relativity

    Recently, in this forum, highly respected members referred to clocks like pendulum and hourglass as if they are relevant for relativity. Are they really? Besides the lack of accuracy, they depend on acceleration/gravity, so they would not work at all in inertial frames and they could not...
  9. Lil123

    Period of a Rod and Disk Pendulum with a variation in how the disk attaches to the rod

    I was able to solve first part I.e. time period of the system when bearing has friction I am unable to figure it out why disk will not rotate when it is mounted to frictionless bearing ? I know that due to absence of friction disk cannot rotate but then Mg is also there which can rotate the...
  10. Asem

    Angular Velocity of a Large Pendulum on Earth as seen from the stars

    I don't understand the question. how am I supposed to find the magnitudes and directions of the velocity from the figure?
  11. C

    I On whether the motion of a Foucault pendulum bob is comparable to ballistics

    A recurring question is: while the motion of a polar Foucault pendulum is fairly straightforward, the case of a non-polar Foucault pendulum is quite difficult to visualize. In 2020, on physics stackexchange someone submitted that question and I contributed an answer. In a comment to another...
  12. M

    Help with Inverted Pendulum on Cart EoM

    Hi All, My goal is to relearn some control theory and implement a working inverted pendulum on a cart with an industrial linear motor. See video: Working through an example of an inverted pendulum on a cart posted here...
  13. C

    Torque calculation for a compound pendulum

    I need to write an equation for Newton's second law for the above system, where k1=k2 (both springs are the same). The red line represents a bar with m=2kg, l=2m. I know that I*α = M1 + M2 + M3 If we displace the bar by x, we get the angle of displacement theta. M1=M2=-k*x I know that...
  14. chris25

    Fictitious forces on a rigid body

    I was confused by how to work this problem in a rotating frame. The solution read that the centrifugal force on the mass should be of magnitude 𝑚𝑤𝑅^2. However, I thought it would be 𝑚𝑤𝐿^2 where L is the distance between the mass and the center of the circle (L = l + R). What am I missing here?
  15. M

    Period of a simple pendulum with a magnet under it

    Hi ... I have answered this question and I think that F/mg equals 3. But I've asked it from someone and he told me that F/mg is 4. Can someone help me find out which one is correct ??? My answer :
  16. L

    Pendulum with a moving support

    In problem 1 I assumed that the suspension moves up and down in an oscillating manner, so ##y_0(t)=Acos(\omega t)## I am not quite sure about task 2, but I would say you can remove the motion of the suspension and the motion of the system would not change noticeably, as I assume that the...
  17. S

    Pendulum Question (Matlab Coursework)

    Apologies for my lack of knowledge on the equations front, I have burnt by brain out on this and haven't the capacity to learn LaTex right now! So here's a screengrab of it: So, This is a Matlab coursework and I am struggling to work out how best to approach solving it. What I have so far is...
  18. D

    Physics project confusion (effects of length on a pendulum)

    We are seeking to design a project where we use a simple pendulum and a motion sensor (that will give us velocity) in order to study centripetal acceleration by essentially changing the length of the pendulum for each trial. This felt simple enough, however our professor insists that we would...
  19. H

    I Alternative Approach to Solving Foucault's Pendulum Behavior

    In many standard texts the behavior of Foucault’s pendulum is solved by adding the Coriolis force term to equation of motion and deriving two coupled differential equations. Here’s an alternative approach: 4 assumptions are made: Mathematical pendulum (point mass attached to massless rigid...
  20. P

    B Calculating g with a Conical Pendulum

    In analysing the conical pendulum, it can be shown that the period is given by T=2pi.sqrt(L.cos(phi)/g) and that therefore, g = 4.pi^2.L.(cos(phi)/T^2). L = pendulum length, phi is measured at the top of the pendulum (at the point of suspension). Graphing cos(phi) vs T^2 should produce...
  21. babaliaris

    For a Pendulum: Knowing Acceleration Find Maximum Angle

    PS: By the way today I had exams in Physics and this problem was the first one I had to solve :p (unlucky) The question was to find the maximum angle θ that the pendulum can reach if we know that the magnitude of the acceleration is the same when the mass is located in the highest and the lowest...
  22. babaliaris

    I Pendulum Tension Force -- How to calculate the full vector?

    Hello! I'm trying to understand how this pendulum works. I found this video that explains how to calculate the T force from the rope. He uses the preservation of kinetic and potential energy in order to find the magnitude of the velocity and then using Newton's second law, he calculates the T...
  23. R

    Classical pendulum homework help please

    Summary: Hi, I'm trying to solve this problem, if it's not right then please help me with a hint without solving it. This formula is just an approximation for small values of theta, but if Vo was greater than the denominator this will lead to large values of theta and then this solution is not...
  24. jackkk_gatz

    Highest point of a pendulum

    I have tried to use the intial velocity v=(2gH)^(1/2) and tried to use conservation of energy, using potential energy to find the maximum height but still can't arrive to the answer provided. Don't know what concepts are relevant here, apparently I can't use velocity neither cosine or sine. I...
  25. Misha87

    B Harmonic oscillator and simple pendulum time period

    Hi, I have been thinking about pendulums a bit and discovered that a HO(harmonic Oscillator) will take the same time to complete one period T no matter which amplitude A/length l it has, if stiffness k and mass m are the same. But moving on to a simple pendulum suddenly the time period for one...
  26. M

    I Motor driven pendulum - How to track its position?

    Hello, On the image below is a test pendelum for rock wool production. The pendelum is driven by two induction motors. When the right motor makes one revolution, the left motor makes two revolutions. The motors are positionally locked (example: when the right motor is at 35.3° the left motor is...
  27. A

    Pendulum made with a Ball and two light strings

  28. AF Fardin

    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
  29. E

    I Solving for the Motion of a Spring Pendulum

    Given the pendulum setup below: Details: ##m## is the mass of the bob ## r ## is the instantaneous length of the spring ## \theta ## is the angle the bob makes w.r.t vertical ## I ## is the bobs mass moment of inertia about pivot ## l_o## is the free length of the spring. ##k## is the spring...
  30. MarkTheQuark

    Mathematica Plotting a parameter Plane of a spring pendulum in Mathematica

    I'm reading an article about the order-chaos-order sequence of a spring pendulum [Ref 1], as I'm reading it I'm trying to reproduce the graphs and results through Mathematica. However, I am new to this software. I will list below some of the most important equations mentioned in the paper. "In...
  31. MarkTheQuark

    Spring-mass system with a pendulum using Lagrangian dynamics

    I'm stuck in a problem of a spring mass system with a pendulum attached to it as showed in the figure below: My goal is to find the movement equation for the mass, using Lagrangian dynamics. If the spring moves, the wire will move the same amount. Therefore, we can write the x and y position...
  32. LCSphysicist

    Normal modes: Spring and pendulum

    I was doing the exercise as follows: I am not sure if you agree with me, but i disagree with the solution given. I was expecting that the kinect energy of the mass ##m## (##T_2##) should be $$T_2 = \frac{m((\dot q+lcos(\theta)\dot \theta)^2 + (lsin(\theta) \dot \theta)^2)}{2}$$ I could be...
  33. G

    Four-Bar Parallel Linkage Pendulum

    Hello, I'm new here and I'm looking for advice regarding some calculations of a device I constructed/should construct. It's a 4 bar (parallel) linkage system, which is used like a pendulum. It is released from a certain height, with just the gravity acting on it. I understand how to calculate...
  34. S

    Period of simple pendulum on an inclined moving platform

    When the platform moves with constant acceleration, the equation of Newton's 2nd law of motion is Forward force - W sin 30o = m.a Forward force = m (a + g sin 30o) ⇒ apparent gravity = a + g sin 30o Final period of pendulum = ##\sqrt{\frac{g}{a+g \sin 30^{0}}} \times 2 = 2.38 s## Is this...
  35. S

    Period of spring-mass system and a pendulum inside a lift

    Based on the formulas, variable ##m , k, L,g## do not change so my answer is (a) but it is not correct. Why? Thanks
  36. VVS2000

    I Damping in a coupled pendulum system

    http://www.cts.iitkgp.ac.in/Phy_1st/Lab_WorkBook/CoupledPendula.pdf This is similar to the experiment which I did
  37. Yossi33

    Physical pendulum time period

    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...
  38. P

    Lagrangian of a double pendulum, finding kinetic energy

    This is from Taylor's classical mechanichs, 11.4, example of finding the Lagrangian of the double pendulum Relevant figure attached below Angle between the two velocities of second mass is $$\phi_2-\phi_1$$ Potential energy $$U_1=m_1gL_1$$ $$U_2=m_2g[L_1\cos(1-\phi_1)+L_2(1-\phi_2)]$$...
  39. S

    Work done on a pendulum by gravity

    Hello guys, I was wondering if someone could provide me some help on this problem. for (c), I know that it will be 0 as the amount of word done from A to B = the am of work done from B to C. But, What I receive as seen in the picture is 2.11N Which is not correct.. In the first try I used a...
  40. Father_Ing

    Cartesian and polar coordinate in Simple pendulum, Euler-Lagrange

    $$L = \frac {mv^2}{2} - mgy$$ It is clear that ##\dot{x}=\dot{\theta}L## and ##y=-Lcos \theta##. After substituting these two equations to Lagrange equation, we will get the answer by simply using this equation: $$\frac {d} {dt} \frac {∂L}{∂\dot{\theta}} - \frac {∂L}{∂\theta }= 0$$ But, What if...
  41. Huzaifa

    B Why is a simple pendulum not a perfect simple harmonic oscillator?

    Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
  42. K

    B Magnetic pendulum and electric energy....

    While reading about electromagnetism from the OpenStax books with my son (and doing some experiments), he asked this question. Suppose I hang a pendulum and make it oscillate inside a coil connected to a Galvanometer as shown in the schematic diagram: Hopefully the image is clear enough. His...
  43. Yossi33

    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]...
  44. J

    Solenoid pendulum frequency

    The flux enclosed by the loop consisting of the solenoid, wires and conducting rod at an angle θ is Φ = blBsinθ, then using small angle approximations and differentiating the induced emf can be found. I know that there must be some torque opposing the motion but am unsure how to proceed.
  45. V

    Kinetic & Potential Energy of a Pendulum

    When the pendulum is released, the Kinetic Energy should be 0. When the pendulum is at the bottom/hits the rod, it should have 0 potential energy. However, I don't quite understand what happens after it hits the rod.
  46. P

    B Pendulum Clock vs GR: Time Discrepancy

    According to general relativity (GR) time runs faster in a weak gravity field relative to a stronger one, for example: clocks run faster at the top of a tall building than at ground level. According to the principle of equivalence the accelerating space elevator should be analogous to gravity -...
  47. GottfriedLenz

    Free body diagram for an inverted pendulum in the rolling sphere

    So, to obtain the motion equations I initially plotted the free-body diagram (see picture). Then I’ve tried to get equations, but I’m not sure, do I have done it rightl. I will be gratefull if someone could help me.
  48. D

    Uncertainty of pendulum period and pendulum length

    I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment? I also need to know the...
  49. D

    Need help with this unequal length bifilar pendulum

    [Mentor Note -- Three threads on the same problem have been merged into this one] Hi, I'm doing a lab report on the relationship between the period of oscillations in an unequal length bifilar pendulum. The set up is like below Can anyone help me derive a formula for the period of oscillations...