# What is Simple pendulum: Definition and 199 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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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. ### Angle that makes kinetic and potential energy of simple pendulum equal

On the first attempt I used conservation of energy to get it down to a single equation involving theta and v (the speed when the angle is theta). But I had no idea how to find v. Now since the maximum speed is given, it is possible to find the maximum angular displacement, ##\alpha##. Then...
2. ### Seeking advice on "simple" pendulum problem

[Mentors' note: moved here from the technical forums after the thread was already fully developed, so no HW template] Hello all! I have a problem which I am beginning to suspect I am either unequipped to solve, or which does not have enough details! I can see, in my mind, the problem, but I...
3. ### 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 :
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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?
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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...
12. ### Simple pendulum subject to a driven force

The problem is how to construct the right diagram of forces actually Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution -mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx'' Fo*cos(wt) = mx'' + mg*x/l + bv
13. ### 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...
14. ### EOM of simple pendulum submerged in a fluid

The question :- My attempt :- The confusion that I am having is that to get the required form of the equation of motion, I had to approximate ##\theta## to be small to get ##x=l\theta## so that I could get the acceleration and the velocity. But, I had to leave the ##sin(\theta)## in the...
15. ### 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.
16. ### 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...
17. ### 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...
18. ### 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...
19. ### Solving the Constrained Lagrangian Dynamics equation for a simple pendulum

The equations is of the form of Differential algebraic Equation, of index 3.
20. ### Sn(u), Jacobi elliptic function, for simple pendulum of any amplitude

I understand how to reach $$\int_0^\phi \frac{d\theta}{\sqrt{1-k^{2}sin^{2}\theta}}=\sqrt \frac g l t$$ from physics but from there I don't get how to turn that into this new (for me) sn(u) form.
21. ### Differential equation for the simple pendulum

How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0## How...
22. ### Max. acceleration of a pendulum changes with its length and mass?

Hi, If I find out the tangential force on the bob at position 1, it turns out to be m*g*sinθ. From this if I find out acceleration by dividing this equation by m, I get only g*sinθ. Does it mean the max acceleration of pendulum has got nothing to do with its length or mass but theta?
23. ### Simple Pendulum: Oscillatory & Periodic Motion

Is the simple pendulum considered to be an example of oscillatory motion or periodic motion or both?
24. ### Angular velocity of a simple pendulum

Homework Statement A pendulum with a light rod of length ##l## with a bob of mass ##m## is released from rest at an angle ##\theta_0## to the downward vertical. Find its angular velocity as a function of θ, and the period of small oscillations about the position of stable equilibrium. Write...
25. ### Simple Pendulum undergoing harmonic oscillation

Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta$$ $$T = mgcos\theta$$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...
26. ### Tension in the string of a simple pendulum

Homework Statement Is the tension in the string of a pendulum, when averaged over time, larger or smaller than the weight of the pendulum? Quantify your answer. You may also assume that the angular amplitude of the oscillations is small. Homework Equations For tension ##T##, angular...
27. ### Elastic Spring / Simple Pendulum Lowest Point

Homework Statement A perfectly elastic spring swings in a vertical plane as a simple pendulum with a mass m suspended at the bottom of the spring. The force constant for this spring is ##k## and the unstretched length is ##L##. The spring is carefully held in the horizontal position so that the...
28. ### Average tension force acting on a simple pendulum

Homework Statement Homework EquationsThe Attempt at a Solution Trying to answer it before solving it, The maximum tension force is mg, so the average has to be less than this. Hence, the option (a) and (c) are not correct. ## T = mg \cos \theta ##, where ## \theta ## is the angle between...
29. ### Swing and angular displacement

hi, we are a few non-native English speaker physics teacher and we wrote some questions for an assessment book but we can't be sure about this two similar question. a) are they accurate for rules of English, are we use correct terms is there a necessary change? b) are they accurate for rules of...
30. ### Simple Pendulum motion - Numerical Integration

Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...
31. ### Simple pendulum - displacement increase

<Moderator's note: Moved from a technical forum and therefore no template.> A simple pendulum of length l (supported by a light, rigid rod) is released from rest at a small angle to the upward vertical. Show that the time taken for the angular displacement to increase by a factor of 10 is...
32. ### Java Runge-Kutta method for Simple pendulum in java

Hi, I'm trying to study Runge-Kutta method and apply on a simple pendulum. Using a timestep dt=0.1 (h=0.1) the pendulum increses energy of 1% every period... while in this site: https://www.myphysicslab.com/pendulum/pendulum/pendulum-en.html decreses energy about 0.01% What am I doing wrong...
33. ### Simple Pendulum: Understand the Relationship Between Theta & L

1. Homework Statement Hey guys, I am reading my Physics book, in that specific section it says "the restoring force must be directly proportional to x or (because x=(theta)*L) to theta" Homework Equations The Attempt at a Solution I have tried to look for that x=(theta)*L relationship...
34. ### Deriving the Simple Pendulum Solution: Second Order and Cosine

Homework Statement Hi guys I am having a problem deriving this solution for a simply pendulum. Could someone please help me. My issue is taking the second order and getting into just cos. I have attempted a solution which is shown below. Homework EquationsThe Attempt at a Solution...
35. ### I Can anyone evaluate this integral?

Hello All! I am trying to solve the simple pendulum without using a small angle approximation. But I end up with this integral: $$\int_{\frac{\pi}{4}}^{\theta}\frac{d\theta}{\sqrt{cos(\theta)-\frac{\sqrt{2}}{2}}}$$ Is this possible to evaluate? If so, could I get a hint about what methods to...
36. ### Why Does T^2 Not Directly Correspond to L in Compound Pendulums?

Hi, I am having some trouble with the following question, any help would be appreciated 1. Homework Statement For a simple pendulum, T^2 is directly proportional to the length of the string (L) Why is this not true for a compound pendulum? Homework Equations T= 2pi sqrt(l/g) [/B]The...
37. ### Lagrangian mechanics, simple pendulum

Homework Statement A simple pendulum of length ξ and mass m is suspended from a point on the circumference of a thin massless disc of radius α that rotates with a constant angular velocity ω about its central axis as shown in Figure. Find the equation of motion of the mass m. Homework...
38. ### Simple pendulum in different situations

Say there is a pendulum which is suspended by a massless thread or rod or whatever, the bob is spherical and hollow. Now consider 2 cases 1) the pendulum is completely filled with water 2) the water inside freezes. will there be a difference in the time periods? If so, why?
39. ### Simple pendulum with Charged bobs

If two simple pendulum with charged bobs hanging from the same point are taken in a satellite ,then their strings will become perfectly horizontal. I think that should be the case when these bobs are charged with similar charges and hence repulsion occurs but what if the bobs are oppositely...
40. ### Maximum Angle of a Simple Pendulum with Given Parameters

Homework Statement A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position. (a) What is the maximum angle away from the lowest position the pendulum will reach? Homework Equations...
41. ### Driven simple pendulum - system of first order ODEs

Homework Statement We have a driven pendulum described by the following differential equation: \frac{d^2\theta}{dt^2} = \frac{-g}{l}\sin(\theta) + C\cos(\theta)\sin(\Omega t) I need to turn this second order differential equation into a system of first order differential equations (then...
42. ### Solving a Simple Pendulum Problem with Math

Homework Statement A 100g mass on a 1.0m long string is pulled 8.0 degrees to one side and released. How long does it take for the pendulum to reach 4.0 degrees on the opposite side? Homework Equations ##T = 2\pi \sqrt\frac{L}{g}## ##x(t) = A\cos\omega t## The Attempt at a Solution From the...
43. ### Solving for the Period of a Simple Pendulum with Given Initial Conditions

Homework Statement [/B] A simple pendulum with l = 9.8m satisfies the equation: \ddot{\theta} + \sin{\theta} = 0 if \Theta_{0} = A Show that the period T is given by: T = \int_0^\frac{\pi}{2}\left(\frac{1}{(1 - \alpha \sin^2{\phi})^\frac{1}{2} }\right)d\phi where...
44. ### Lagrangian and Euler-Lagrange of a Simple Pendulum

Homework Statement A simple pendulum with mass m and length ℓ is suspended from a point which moves horizontally with constant acceleration a > Show that the lagrangian for the system can be written, in terms of the angle θ, L(θ, θ, t˙ ) = m/2(ℓ^2θ˙^2 + a^2t^2 − 2aℓtθ˙ cosθ) + mgℓ cos θ >...
45. ### Simple pendulum: Determine the velocity

Homework Statement A homogeneous bar with length 0.6 m and mass m = 2 kg is fixed to a wall via a hinged connection in the vertical plane. At the end of the bar a constant force F acts of 150 N. The bar is released from the vertical equibrilium position. Determine the velocity (of the COG) and...
46. ### Simple pendulum and acceleration due to gravity

Homework Statement A simple pendulum and a mass-spring system have the same oscillation frequency f at the surface of the Earth. The pendulum and the mass-spring system are taken down a mine where the acceleration due to gravity is less than at the surface. What is the change in the frequency...
47. ### Simple Pendulum in Free Fall: Surprising Motion and Video Evidence

Homework Statement This is a 'random discussion' that I had today with a student; it is not out of a textbook, nor does the solution carry any weight at all (pls excuse pun).[/B] A simple pendulum is happily swinging back and forth attached to a pin in the wall of the lift, where the pin is...
48. ### MHB Simple pendulum, ref: POTW 156

I was waiting for the http://mathhelpboards.com/potw-university-students-34/problem-week-156-march-23-2015-a-14734.html for University students solution to be posted before I asked this question. I ran across this problem as I was trying to solve the problem and I got stuck rather quickly. The...
49. ### Time to Reach Highest Speed of Simple Pendulum

Homework Statement You pull a simple pendulum of length 0.260m to the side through an angle of 3.50∘ and release it. Part A: How much time does it take the pendulum bob to reach its highest speed? Part B: How much time does it take if the pendulum is released at an angle of 1.75∘ instead of...
50. ### Simple Pendulum Project: Amplitude's Effect on Period | Math Help Included

nee help with project dealing with simple pendulum.I am supposed to be looking at the effect of changing the amplitude and how it affects the period. The requirements want to show some math( it does not include finding average and error). Need help. what could I show there. Like the time to...