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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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. aatari

    Finding the Uncertainty in the motion of a pendulum

    Hi guys can someone look at my work for uncertainty and let me know if it makes sense.
  2. F

    Equation Demonstration -- Simple Pendulum Analysis

    I've just studied simple pendulum: The simple pendulum (for small oscillations) differential equation is first image. I've no problem to arrive this result and formula. My problem is to get to the second formula by passing through another formula (Image 3) that my book mentions. I can't...
  3. LCSphysicist

    Find the Lagrangian of a pendulum plane

    Pendulum plane, which suspension executes a horizontal harmonic motion $$x = acos(\gamma t)$$ Position P, orientation x to right and y points below, phi is the pendulum's angle wrt y. $$P = (acos(\gamma t) + lsin(\phi(t)), lcos(\phi(t)) )$$ So executing all that is necessary, i found it...
  4. I

    Period of a Pendulum on the Moon

    The equation that governs the period of a pendulum’s swinging. T=2π√L/g Where T is the period, L is the length of the pendulum and g is a constant, equal to 9.8 m/s2. The symbol g is a measure of the strength of Earth’s gravity, and has a different value on other planets and moons. On our...
  5. T

    Lagrangian mechanics, system of a spring and a pendulum

    Hello! I have some problem getting the correct answer for (b). My FBD: For part (a) my lagrangian is $$L=T-V\iff L=\frac{1}{2}m(b\dot{\theta})^2+mg(b-b\cos\theta)-\frac{1}{2}k\boldsymbol{x}^2,\ where\ \boldsymbol{x}=\sqrt{(1.25b-b)^2+(b\sin\theta)^2}-(1.25b-0.25b)$$ Hence my equation of...
  6. archaic

    Solving a Pendulum Problem with Exponential Solution

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  7. badluckmath

    A simple pendulum is suspended from the ceiling of an accelerating car

    Here is an image of the problem: The problem consist in finding the moviment equation for the pendulum using Lagrangian and Hamiltonian equations. I managed to get the equations , which are shown insed the blue box: Using the hamilton equations, i finally got that the equilibrium angle...
  8. badluckmath

    A simple pendulum is suspended from the ceiling of an accelerating car

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  9. Justinboln

    Calculate the New Velocity and the Velocity of a Pendulum Mass

    Question 1: A pendulum 2.2m long has a mass of 8.5kg suspended from it. The pendulum is initially in a vertical position and is moved to new position 35 degrees from the vertical. (a) How much work is required to move the pendulum to its new position? (b) If the pendulum swings from this...
  10. BayMax

    Double pendulum equations of motion using Newton's laws

    I need help to understand this problem taken from Mechanical Vibrations by S. Rao I know that the equations of motion could be obtained in various ways, for example using the Lagrangian, but, at the moment, I am interested in understanding the method he used. In particular, if I'm not...
  11. LCSphysicist

    Oscillations with fluid and pendulum

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  12. LCSphysicist

    Simple pendulum subject to a driven force

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  13. N

    T-Shaped Pendulum: Find the Total Mechanical Energy

    My answer to part A is correct but for Part B I got an incorrect answer of 0.204J. My working out is sent as an attachment. Part A: Part B: Part C:
  14. anuttarasammyak

    Energy transfer and conservation cases for pendulum motion and EM wave

    Let me ask a very primitive question. To and fro motion of pendulum under gravity tells us potential energy + kinetic energy = const. At the top points potential energy: max kinetic energy :0 At the bottom point potential energy: 0 kinetic energy :max EM wave is usually illustrated as...
  15. jjson775

    How can I accurately calculate the quantum number of a pendulum?

    Summary:: Calculate the quantum number of a pendulum I want to calculate the quantum number of pendulum. L = 1m, m = 1 kg., A= 3cm. I get a period of 2.01 sec. and f = 1/T = .498 sec. E =nhf gives me 2.67x10^31. The correct answer is 1.33x10^31, Where am I going wrong? [Thread moved from...
  16. DerbisEternal

    How do I proceed with two different trig functions containing x on the left?

    Given the total angles in the x direction, I set up this: (mg/cos(x))*sin(x)-Fe=0 then isolated for x: mgtan(x)=(kq^2)/(2*sin^2x) sin^2(x)*tan(x)=(kq^2)/(2mg) From here I am stuck. How do I go forward when x is contained in two different trig functions on the left?
  17. LCSphysicist

    Find the period of a pendulum consisting of a disk of mass M

    I did the first step pretty well, and the answers match, but i don't understand why in the second case the period changes.
  18. D

    Simple pendulum of variable mass

    Hello, I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant). I approached this with lagrangian mechanics, asumming the positive ##y## direction is...
  19. D

    Phase space of a harmonic oscillator and a pendulum

    Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
  20. LCSphysicist

    Period of Pendulum: Spinning Disk Forces & Inertia Moment\

    If the bottom disk is free to spin, will it necessarily spin? all the forces in this disk don't produce a torque. I don't know why we disregard it's inertia moment when it is free to spin (It's intuitively set, but I can't see it mathematically) :\
  21. LCSphysicist

    Two-Disk Pendulum Oscillation: Find Period w/ Mass M & Radius R

    "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 centers are a distance I apart. Find the period for small oscillation" I don't understand why we...
  22. SilverSoldier

    Differential Equation for a Pendulum

    Suppose we displace the pendulum bob ##A## an angle ##\theta_0## initially, and let go. This is equivalent to giving it an initial horizontal displacement of ##X## and an initial vertical displacement of ##Y##. Let ##Y## initially be a negative number, and ##X## initially be positive. I observe...
  23. aligator11

    Engineering Homework problem - Pendulum oscillatory system

    Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.
  24. brotherbobby

    Work done on a conical pendulum

    The diagram for the problem is shown alongside. In the vertical (##\hat z##) direction we have ##T \cos \theta = mg##. In the plane of the pendulum, if we take the pendulum bob at the left extreme end as shown in the diagram, we have ##T \sin \theta = \frac{mv^2}{r}## (the ##\hat x## axis of...
  25. P

    Conical pendulum: what are the tension and the angle?

  26. PickyBiker

    Understanding Force vs Speed for Arduino-Based Inverted Pendulum on Cart

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  27. Z

    Confused about how to find the mean of uncertainties for pendulum exp.

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  28. Saptarshi Sarkar

    EOM of simple pendulum submerged in a fluid

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  29. VVS2000

    Compound pendulum experiment to find the acceleration due to gravity

    In this experiment, I still can't figure out why the graph between time period and distance from point of oscillation is like that. Why does it first decrease and increase so steeply? I got the second part because it goes near the centre of gravity and time period becomes almost infinite there...
  30. Saptarshi Sarkar

    Order of anharmonicity of a simple pendulum

    I know that the potential of a simple pendulum is given by the above formula and that we can expand ##cos\theta## to get ##V=mgl\left(\frac{\theta^2}{2}-\frac{\theta^4}{24}+...\right )## I am guessing that the answer is ##\theta^4##, but I am not sure what "order" means here.
  31. Saptarshi Sarkar

    Solution for the exact pendulum

    The question is My attempt is given below I am not sure what to do now. I don't understand how I can make the coefficient of ##cos\theta## negative.
  32. B

    Is 51 micro joules the maximum kinetic energy of this pendulum?

    So I have been given a question here which asks me to work out the maximum kinetic energy of the pendulum It has given info such as time period and amplitude, which I had then made use of these formulas Does a kinetic energy of approx 50.98 micro joules seem right here? Any help would be...
  33. Kaushik

    B Forced Oscillations: Pendulum 1 Driving Neighboring Pendulum

    Consider the following setup: In this, let us set the pendulum 1 into motion. The energy gets transferred through the connecting rod and the other pendulum starts oscillating due to the driving force provided by the oscillating pendulum 1. Isn't it? So the neighbouring pendulum starts...
  34. S

    Conical Pendulum: Solving the Height Issue

    So in this instance height is longer than the 3m string which is impossible. Do we just say that when ever H>L, H=L?
  35. Curious_Student

    Mechanics Lab | A Simple Pendulum & a Small Magnet Underneath

    I have measurements of period time and distances that's all: T (sec) D (m) 0.9 0.008 0.91 0.009 0.97 0.01 0.98 0.011 1.06 0.012 I thought about adding the magnetic force like: T=2π*√l/(g+x) but have no clue how to integrate the distance there, I don't know even how to start...
  36. J

    Motion of 2 masses connected by a rod to a pendulum

    I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.
  37. rzyn

    Rotation and effective gravity on Earth

    I'm interested in calculating effective gravity for a point-mass in a spinning gyro or swinging pendulum bob on a rotating planet undergoing any translational velocities and/or accelerations. I want to investigate the theoretical effects of high-energy mechanical oscillation on orbital...
  38. Prabs3257

    Change in the time period of a pendulum

    I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer
  39. JD_PM

    Equation of motion of a simple pendulum

    The equation of motion of a simple pendulum is: $$\ddot \theta + \frac{g}{l} \theta = 0$$ Our Physics professor told us: 'If you want to become a good Physicist you have to be able to analytically check your answers to see whether they make sense'. In class he took the limits of constant...
  40. JD_PM

    Man rotating in a merry-go-round and grabbing a pendulum

    Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...
  41. Q

    Coupled pendulum with external force?

    I got this picture from a superconducting parametric amplifier text I was reading. (The picture is a mechanical analog of a non-degenerate parametric amplifier.) If the balls(red and blue) were oscillating at their own natural frequencies, and an external force is driven(purple), how would the...
  42. velocityoverrtime2

    How do I calculate the time and distance for a pendulum projectile problem?

    Tried to find time in seconds in order to use the formula d=vt and find the distance in the x plane in which the target must be placed, to no avail.
  43. S

    Spring pendulum with and without weight

    Equations provided: for a spring pendulum and m replaced with L and k with g for the same pendulum, but with no weight attached. Greetings I tried solving this by stating that the length is 0,50m (since no length of the spring is given) and turning around the equation for the spring...
  44. T

    How to Calculate Instantaneous Impact Force in a Pendulum Impact Tester?

    Hi there, First of all i want to apologize for my english, but i am not from english speaking country, so i am not perfect in it. Now for the question. I need to calculate instantaneous impact force in the lower dead center of Charpy hammer knowing nominal potential energy in lower dead center...
  45. S

    Understanding T^2 x L Graphing for Simple Pendulum Experiment

    Summary: Question regarding graphing a T^2 x L graph for a simple pendulum I did a Simple Pendulum experiment in my college physics class the other day. We were asked to graph a T^2 x L graph based off our results. I plan on using the Length on the x-axis and the T^2 on the Y-axis. This may...
  46. A

    Solving the Constrained Lagrangian Dynamics equation for a simple pendulum

    The equations is of the form of Differential algebraic Equation, of index 3.
  47. jisbon

    Angular velocity of a pendulum

    So this question has something probably due to the conservation of angular momentum. I am able to find the moment of inertia about the pivot, which is : $$\dfrac {1}{3}mL^{2}+\left( \dfrac {1}{12}ML^{2}+mL^{2}\right) =\dfrac {17}{12}ml^{2} $$ Now to find angular velocity when angle =0, how am I...
  48. F

    Inverted pendulum -- What force is applied at the center of mass?

    Summary: I know that in order to keep inverted pendulum balanced when it leans forward, I should accelerate the bottom of it, but what is the force which is applied to center of mass of the pendulum with balances torque due to gravity? Is it inertial force? We assume that our inverted pendulum...
  49. F

    Segway balance question (inverted pendulum)

    Summary: Why does segway rider who leans forward when accelerating keep balanced ? Is it because the inertial torque acting on the rider balances the torque created by gravity? F=-ma
  50. F

    Solving the Rocket Pendulum Fallacy?

    I have been researching the rocket pendulum fallacy and have gotten into some spirited debate on the subject. If I understand correctly... 1. if the thrust is perfectly in line with the centerline (and no outside forces act on the craft other than gravity) it does not matter where the source...
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