What is Pendulum: Definition and 1000 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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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. 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...
  2. 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...
  3. 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 30oFinal period of pendulum = ##\sqrt{\frac{g}{a+g \sin 30^{0}}} \times 2 = 2.38 s## Is this...
  4. 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
  5. 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
  6. 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...
  7. 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 $$U_1=m_1gL_1$$ $$U_2=m_2g[L_1\cos(1-\phi_1)+L_2(1-\phi_2)]$$...
  8. 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...
  9. 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...
  10. 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?
  11. 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...
  12. 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]...
  13. J

    Can Resistance Determine the Torque in a Solenoid Pendulum System?

    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.
  14. 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.
  15. 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 -...
  16. 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.
  17. 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...
  18. 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...
  19. hello_world30

    I Proving that ##\omega_0^2 < 2g/l ## for a simple pendulum.

    Here is the problem : A pendulum is composed of a mass m attached to a string of length l, which is suspended from a fixed point. When hanging at equilibrium, the pendulum is hit with a horizontal impulse that results in an initial angular velocity ω0. Show that if ω20 < 2g/l, the string will...
  20. Peter Jones

    I How does a large-angle pendulum oscillate?

    So in high school i studied the small oscillation of a simple pendulum with no air resistence. It reaches harmonic oscillation when the angle is small enough, so it is an approximation right? But what happens if the angle isn't small, will it still oscillate and how? According to energy...
  21. M

    A Lagrangian for a double spring pendulum connected through a rigid bar

    Hi Guys I am looking for some guidance with regards to a Lagrangian problem I am trying to solve. Please refer to the attached documents. Please neglect all the forcing functions for the time being. I am currently just trying to simulate the problem using initial conditions only I have...
  22. S

    Height of pendulum after hitting a peg

    By considering conservation of energy, my answer is (B). But the solution states the answer is (A) Is it because there will be loss of some of the KE when the string hits the peg so making answer (A) is better than answer (B)? The question itself does not state about friction Thanks
  23. L

    Amplitude of oscillation of a mass which is the pivot of a pendulum

    1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and...
  24. p1ndol

    I Understanding the Coordinates in the Lagrangian for a Pendulum

    So I've been studying classical mechanics and have come across a small doubt with the solution provided to the problem in question from Landau's book. My question is: why are the coordinates for the particle given as they are in the solution? I imagine it has something to do with the harmonic...
  25. H

    How can I design a Foucault Pendulum for my university building?

    Hi guys, I think I have persuaded the administration to install a Foucault pendulum in my university building where a high roof and open spaces are available. The thing is I have to project it with design, cost, etc. Those are domains which I don't have much expertise as a simple physicist. So...
  26. Ang09

    Moment of Inertia with varying distance from Centre of Mass

    h = d1 + 0.08 d1 = h - 0.08 d2 = h + 0.08 I of the vertical portion = 1/12 m (l^2 + b^2) + md1^2 = 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2 I of the horizontal portion = 1/12 m (l^2 + b^2) + md2^2 = 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2 The moment of inertia for the whole T-shape about...
  27. S

    Inverted pendulum on a cart using a PID controller

    hi everyone. in my project , I'm facing with a problem. in PID controller , desire poles are -1+j3 & -1-j3 after design , the overshoot is very high and the settling time more than PD controller i change the K and zi (pi) several times . but not better. the pd controller : (s+23) pid controller...
  28. Abhisheko07

    Fortran Spring Pendulum system in FORTRAN

    I have checked the program several times the program is running but the graphs I am getting is not what I was accepting soon one of the variables approaches zero I don't know why is it happening. The program I have made is below and it's in the FORTRAN language. If anyone knows Fortran can they...
  29. S

    Practice Problem about the Energy of a Pendulum

    Answer: a) 7.35 m/s b) 216.09 m/s^2 *Is this correct?
  30. Chestermiller

    Time Average Value of Pendulum String Tension

    Another member and I, in private conversations, have been discussing the time average tension in a pendulum string. He has done a numerical analysis of the problem, and his calculations indicate that the time average tension is less than mg. I have analyzed the problem analytically by...
  31. Zenon

    What is the relationship between a rocket and Inverted Pendulum?

    I'm doing my homework about the Inverted Pendulum and I'd like to know how a rocket flies and why it's related to an Inverted Pendulum.
  32. hang

    Pendulum with Spring | Buy Now

  33. hang

    Seesaw with spring and plate

  34. Y

    Rolling pendulum angular acceleration

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  35. HansBu

    Stability of a Driven Pendulum

    I understand that when $$A_0 \gg g$$, the g term in the equation of motion can be dropped. The equation of motion then becomes $$\frac{d^2\theta}{dt^2}=-\frac{a_d(t)}{L}\sin\theta$$ But how can I show that the pendulum is stable for such case? I am totally clueless.
  36. C

    Wall made of Pendulum -- thought experiment

    If your house wall is made of pendulum or a ball attached to a string on top. It won't attract seismic forces. Whereas if the wall is fixed solid. It can attract seismic forces. What is the physics explanation of it? Is it because you try to deflect momentum or inertia? What is the right...
  37. T

    Why Does Second Collision in Ballistic Pendulum Lead to Initial State?

    I was thinking about ballistic pendulums and the symmetry they exhibit. In the simplest case, you have one ball that begins at a certain height and collides with another ball at rest. You can calculate via conservation of momentum and energy the new velocities and max vertical displacements...
  38. H

    Finding the Oscillations of Pendulum A

    First of all, I found the angular frequencies for both pendulum and breathing mode which are ##\omega_p = 4.95## ##\omega_b = 7.45## Then I found the normal mode coordinates equations: ##q_p(t) = A cos \omega_p t## ##q_b(t) = B cos \omega_b t## And the beating frequency (I'm not sure if I...
  39. D

    Lagrangian of a mass bewteen two springs with a pendulum hanging down

    What I first did was setting the reference system on the left corner. Then, I said that the position of the mass ##m_2## is ##x_2##. I also supposed that the pendulum makes an angle ##\theta## with respect to the vertical axis ##y##. So the generalized coordinates of the system would be ##x_2##...
  40. momoneedsphysicshelp

    Solving for the velocity of a Pendulum

    I think the answer is 6.2 but I also got 40m/s. Which one is right?
  41. HansBu

    Solving Damped Driven Pendulum ODEs

    Here are the nonlinear and coupling ordinary differential equations: I was given values of a, b, and c as well as some initial values for x, y, and z. If ever the equations above are related to the pendulum, I can think of a as the damping factor, b as the forcing amplitude, and c as the...
  42. Rafums

    How to calculate acceleration of blobs in any degree pendulum?

    I want to create a method to calculate acceleration of blobs in any degree pendulum (double, triple and more). I have this equation but I am not sure if it is correct, or how to extract acceleration from it. [Mentor Note -- this is a new thread start to correct errors in the previous 2 thread...
  43. brotherbobby

    Pendulum hung from the ceiling of a train

    (a) No, a person seated inside the train compartment will not be able to tell whether the train is accelerating on a horizontal track or moving uniformly up an inclined track by observing the plumb line. (b) I am assuming that both observers are not allowed to look "out" of the boundaries of...
  44. A

    Conical Pendulum with varying string length

    Consider a conical pendulum like that shown in the figure. A ball of mass, m, attached to a string of length, L, is rotating in a circle of radius, r, with angular velocity, ω. The faster we spin the ball (i.e., the greater the ω), the greater the angle, θ, will be, and thus, the smaller the...
  45. yucheng

    Component forces of a pendulum

    I refer to the website below (for more information): http://www1.lasalle.edu/~blum/p106wks/pl106_Pendulum.htm#:~:text=The forces acting on the,the tension of the string.&text=The net radial force leads,is v2/r.) P.S. I'll insert my specific questions in the following paragraphs in this format...
  46. bieon

    Pendulum, Rotational Inertia and Center of mass

    This is the figure given. My Attempt ##T=2\pi \sqrt\frac {I}{0.5gd}## ##\frac {m_r} {l} ## ##dm= \frac {m} {l}dx## ##dI = dm_r x^2## ##dI=(\frac {m_r} {l}dx)x^2## ##I= \int_l^0 (\frac {m_r} {l}dx)x^2 \, dx ## ##I_c.m=\frac {m_r l^2}{3}## ##I_,, = \frac {m_r l^2}{3}+m_p x^2## Given...
  47. Daniel Boy

    Motion Equations by Newton's Formalism for a Double Pendulum

    By Lagrange's formalism, the motion equations for double pendulum are: Using Newton's formalism I can't obtain the second equation. Anyone can help?
  48. PaBlo14101066

    Lagrangian function of a double undamped pendulum

    I must find the Lagrangian for an undamped pendulum using the diagram showed below, I've no idea what to do with the second angle φ2 because is measured from the line that joins the two pivot points. The ecuations I must obtain are as follows I get so many different things but I can't reach...
  49. H

    Plane pendulum: Lagrangian, Hamiltonian and energy conservation

    Hello! I need some help with this problem. I've solved most of it, but I need some help with the Hamiltonian. I will run through the problem as I've solved it, but it's the Hamiltonian at the end that gives me trouble. To find the Lagrangian, start by finding the x- and y-positions of the...
  50. A

    Exploring the Relationship Between Amplitude and Time in a Pendulum Clock

    Hello! So we are given this very interesting physics question, that we should only discuss and not do any calculations. So for a) I've though this if the clock is running too fast,the way to adjust this would be to lengthen the pendelum length,my logic behind this the longer the pendelum the...
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