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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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

    Conical pendulum in rotating frame

    Homework Statement A pendulum of length l at the north pole is moving in a circle to the east at an angle \theta to the vertical. It has some period T_E as measured in the rotating Earth frame. The experiment is then repeated except now the pendulum is moving to the west with period T_W...
  2. A

    Calculating error in pendulum motion

    Homework Statement I have to calculate the propagated error on g of pendulum. I pretty much measured the T of pendulum and now calculating g while increasing the number of cycles. Homework Equations I used the equation of propagated error and i included picture of it and my calculations. The...
  3. T

    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...
  4. StrangelyQuarky

    How Do You Derive the Period of a Pendulum with Arbitrary Amplitude?

    Homework Statement A pendulum obeys the equation \ddot{\theta} = -\sin(\theta) and has amplitude \theta_0 . I have to show that the period is T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{\sqrt{1-\alpha \sin^2(\phi)}} where \alpha = \sin^2(\frac{\theta_0}{2}) 2. The attempt at a solution...
  5. J

    Elementary pendulum equation of motion

    Homework Statement To find the period of oscillation of the pendulum and the equation of motion. Homework Equations Conservation of energy. Potential energy in a constant field = mgh. Kinetic energy in polar coordinates with r constant = (1/2) m r2 (dΘ2/dt2) The Attempt at a Solution I won't...
  6. LLT71

    Solving Pendulum Confusion: m*a=-k*x Explained

    I find it somehow confusing to imagine why m*a=-k*x is "generally valid". that minus sign bothers me. Imagine I raised a bob to some height (ex. from the left side) and then released it. from that moment till the moment where it reaches equilibrium position m*a and restoring force have same...
  7. T

    2008 us physics olympiad pendulum in electric field

    1. Homework Statement i was solving the 2008 semi final us physics olympiad paper when i got stuck on question B2 in part 2 http://www.aapt.org/Programs/contests/upload/olympiad_2008_semi-final_soln.pdf the link takes you a pdf with questions and solution however i don't understand the soution...
  8. J

    I Connection between Foucault pendulum and parallel transport

    Hello! I try to think about the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel transported represents(for example, is it the normal to the plane of oscillation vector?). In...
  9. V

    How Does a Pendulum on a Rotating Arm Behave When the Arm Stops?

    Scenario There is a pendulum suspended on an arm that rotates a certain angle in the horizontal plane. The arm suddenly stops, how far will the mass of the pendulum be displaced in the horizontaly? Thought so far: The momentum of the arm will be L=IW and when it stops I think the mass at the...
  10. CK_KoopaTroopa

    How to find torque of rotational friction on an axle?

    Hi, I'm trying to program a simple physics engine from scratch as an exercise, and I'm starting with manipulating a stick with the mouse pointer. As of now, it dangles from one end demonstrating simple pendulum physics. Now, I want to add a friction component to the "axle" it's rotating on to...
  11. C

    Tension in a Pendulum: Exploring Horizontal Component and Restoring Force

    1. The problem statement, all variables and given/knowns So basically,I am confused by this quote in David Morin's Problems and Solutions in Introductory Mechanics that says: the tension in the tilted string has a nonzero horizontal component (except at the highest points where the tension is...
  12. Kernul

    Conic Pendulum Exercise: Tension and Velocity as Functions of Angle

    Homework Statement A tether ball of mass ##m## is suspended by a rope of length ##L## from the top of a pole. A youngster gives it a whack so that it moves with some speed ##v## in a circle of radius ##r = L sin(\theta) < L## around the pole. a) Find an expression for the tension ##T## in the...
  13. U

    Muzzle Velocity by Analyzing Ballistic Pendulum

    Homework Statement Finding the equation for the muzzle velocity by using conservation of energy. 2. The attempt at a solution Ek+Eg=Ek2+Eg2 Well I'm 100% sure the kinetic energy of the ball is transferred into the catcher. The displacement is 1.9cm which is 0.019m. Mb=0.0077Kg (mass of ball)...
  14. jakec

    Momentum conservation (ballistic pendulum)

    Homework Statement A .01kg bullet is fired into a 1.2kg block hanging from a 1m wire. The bullet exits the block with a speed of 200m/s and the block swings to a height of .2 meters. What is the original velocity of the bullet? What percentage of the original energy of the bullet is no longer...
  15. L

    How high does a pendulum go after pushing at equilibrium?

    Usually, the pendulum problems I encounter relate to initial velocity. What happens if, at equilibrium, I push a pendulum with a certain amount of force? (E.g. 10N) Is there a way to calculate how high the pendulum will go? I guess it's complicated considering torque done by gravity, etc
  16. Andy Froncioni

    Rolling Pendulum: Solving the Dynamics Equations

    (This is NOT a homework problem. It's an engineering problem I'm trying to crack.) A wheel with a rubber tire (friction) can roll on a suspended rail. Attached to it is a pendulum that's rigidly mounted on the axle of the wheel with a mass that can hand down and swing. (The wheel's rotation...
  17. L

    Pendulum in vacuum vs with air resistance

    If a pendulum consisting of a string and a bob is allowed to swing in a vacuum vs in air, which has larger period?
  18. R

    Period of pendulum moved to Jupiter's moon Io

    Homework Statement you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s Homework Equations T=2*π√l/g[/B]The Attempt at a Solution T1/T2=√(g2/g1)
  19. D

    Applications of coupled pendulums

    I have done an experiment changing the mass ratio of coupled pendulums. To conclude I need real world applications for the coupled pendulums. But, i cannot find it online. So, it would be really helpful is someone could give examples of this. THANKS!
  20. Euler2718

    MATLAB "Linear Model" of a Pendulum via Euler's Method

    In my problem the linear modal is defined as the first term in the series expansion of \sin(x) so: \sin(x) = x - \frac{x^{3}}{3!}+\dots \sin(x) = x is the linear modal. So with this, I then have to write \frac{d^{2}x}{dt^{2}} = -\sin(x) as a system of x^{\prime} and y^{\prime}, so...
  21. FallenApple

    How does pendulum go slack above the horizontal?

    So say a pendulum consisting of a non rigid string and mass bob is swung above the horizontal position. It's given an impulse at the bottom so that in the swing, there is nothing but tension and gravity acting. At above the horizontal, the gravity is pointing down while the tension can only...
  22. tony873004

    Determining the period of a pendulum with an accelerometer

    I've got an accelerometer swinging back and forth on a string collecting data. But because of the tolerance of the accelerometer, the data is not quite clean enough to simply determine when positive turns to negative, or passes through equilibrium. Here's the data. (arbitrary reading vs. time...
  23. dykuma

    Lengthening Pendulum Homework: Working with Equation 18.1

    Homework Statement Homework Equations The Attempt at a Solution Working with equation 18.1 i found that However, this obviously is not the equation in 18.3. I found a source talking about this problem, and they get a similar equation http://file.scirp.org/pdf/JAMP_2014031310562629.pdf I...
  24. O

    Elastic Pendulum with Newton's equations of motion

    Homework Statement A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...
  25. A

    Finding the force of constraint--compound pendulum on spring

    Homework Statement From Fetter and Walecka 5.1:[/B] Consider the compound pendulum in FIg 28.1 (mass M, moments of inertia Iij relative to the center of mass, which is a distance L from the point of support Q) but with Q attached to the bottom of a vertical spring (force constant k) and...
  26. angrymasteryoda

    Pendulum swinging and hitting a peg

    Homework Statement a pendulum of mass m and length L is pulled back an angle of θ and released. After the pendulum swings through its lowest point it encounters a peg α degrees out and r meters from the top of the string. The mass swings up about the peg until the string becomes slack with the...
  27. J

    Elastic collision with pendulum

    Homework Statement A steel ball of mass 0.890 kg is fastened to a cord that is 50.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal, as shown in the figure. At the bottom of its path, the ball strikes a 2.50 kg steel block initially at rest on a...
  28. Brad Meacham

    Foucault's Pendulum Recreation for Physics Project

    (I apologise if this is the wrong area to post) Hello everybody I am planning on building my first Focault Pendulum(As a physics projject for school) and I have a few questions. I am going to purchase a cable(it needs to be smooth and friction-less around 7 feet), I also am going to need to...
  29. B

    What is the magnitude of gravity of a pendulum that is moved

    << Mentor Note -- OP correctly re-posted schoolwork question in the HH forums; threads merged >> The full question is: The pendulum inside a grandfather clock has a half period of 1.0000s at a location where the magnitude of the local acceleration of gravity is 9.800 m/s^2. The clock carefully...
  30. michaeldk

    Pendulum fallacy - hovering rockets, still applies?

    Hi all! I've come here to seek your expertise because I've ran into a bit of a heated discussion (well, heated from the other side ;-) about rockets, hovering and center of gravity. Basically people are referencing to the pendulum fallacy when I say that a rocket which is hovering would be...
  31. J

    Finding the radius of a pendulum

    Homework Statement A monkey is swinging a coconut of 1 k in a pendulum like motion. When the monkey's motion is at the bottom of its swing it is .6 m above the ground. He releases the coconut when it it is in this position when the force is 250 N and it travels 10 meters before hitting the...
  32. J

    Pendulum Projectile: Find Direction of Travel Formula

    Homework Statement This isn't a specific problem, I just wondering if there was a formula to describe the direction of travel an object would take if it was part of a pendulum and the string broke. Homework EquationsThe Attempt at a Solution Seeing that if the string broke in the instant that...
  33. S

    Pendulum experiment systematic errors

    Homework Statement So we had to the simple pendulum experiment and were measuring the effect of the length of the pendulum on its period of motion. However, our results produced a line of best fit that was significantly higher than the expected line of best fit (with length vs period squared)...
  34. J

    Lagrangian of a double pendulum system (with a spring)

    Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...
  35. E

    Conservation of Energy of Mass on Crane

    Homework Statement A mass is suspended from a crane by a cable of length L. The crane and the mass is moving at constant speed V. The crane stops and the mass on the cable swings out. What is the angle that the mass swings? If the angle is 50 degrees and L=6m, what is the initial speed of the...
  36. AAO

    Cart with Pendulum | Tension expression

    I am trying to derive an expression for the Tension T in the massless bar in the given photo. Where there is a cart that is moving only in the x-direction and the bar is rotating around a point pivoted at the cart with angle theta. The expression that I have is deduced from: ∑ F (towards...
  37. mmcsa

    Determining linear velocity of pendulum

    Hello, I'm trying to develop a pendulum to test protective equipment so I want to work out the length I'll need to generate a desired velocity and the necessary mass I'll need for a specific moment of inertia. I know there are multiple ways to solve for linear velocity with equating Ek and Ep...
  38. S

    Angular acceleration of Pendulum equation

    Is this a legitimate equation? θ'' = − g⁄R sin θ Source: ftp://www.myphysicslab.com/pendulum1.html ftp://www.myphysicslab.com/images/pendulum_2.gif The pendulum is modeled as a point mass at the end of a massless rod. We define the following variables: θ = angle of pendulum (0=vertical) R =...
  39. Hamal_Arietis

    Large oscillations of pendulum

    Homework Statement Find the large oscillation period T of pendulum. Suppose that the amplitude is ##\theta_0## We can write oscillation period T by the sum of a series, know that: $$\int_0^1 \frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}=\frac{\pi}{2} \sum_{n=0}^{∞}(\frac{(2n)!}{2^{2n}(n!)^2})^2$$ Let...
  40. T

    Pendulum equation/expression, manipulation Help

    Homework Statement Converting the simple pendulum expression for g in terms of the angular frequency ω instead of the period T, where ω=2π/T, yields g=ω2L. Derive an expression for the error (Δg) in g by first setting g=A⋅B. A= B= Therefore in terms of A, ΔA, B, and ΔB: Δg/g= Converting back...
  41. S

    Large Amplitude Pendulum Equation

    The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?
  42. Hamal_Arietis

    I Large oscillations of pendulum

    When I solve this problem i have the equation: $$x''+Asinx=0$$ How solve this equation if x large? I think we use some approximations
  43. Y

    Lagrangian for a Spherical Pendulum (Goldstein 1.19)

    Homework Statement Find the Lagrangian and equations of motion for a spherical pendulum Homework Equations L=T-U and Lagrange's Equation The Attempt at a Solution [/B] I found the Lagrangian to be L = 0.5*m*l2(ω2+Ω2sin2(θ)) - mgl*cos(θ) where l is the length of the rod, ω is (theta dot)...
  44. andrespinilla

    Pendulum is vibrating freely in unforced oscillation

    When the pendulum in Problem 3.8 is vibrating freely in unforced oscillation, the amplitude of its swing decreases by a factor of e after 75 cycles of oscillation. (a) Determine the Q-value of the pendulum. (b) The point of suspension of the pendulum is moved according to ξ = a cos ωt at the...
  45. R

    How to Prove that a Flying Pendulum follows SHM

    Hi, I was wondering if someone could please help me to understand : 1) How can I prove that a Pendulum is following SHM? 2) Also, does being isochronous also mean that the pendulum is following SHM? Thank You very much.
  46. S

    Spherical Pendulum - elliptic integral

    Hello everyone. In the 3rd edition of Mechanics by Landau and Lifshitz, paragraph 14, there is a problem concerning spherical pendulum. Calculations leading to the integral $$ t=\int \frac {d \Theta} {\sqrt{\frac{2}{ml^2}[E-U_{ef}(\Theta)]}},$$ $$...
  47. P

    Trajectory of pendulum in frame of rotating disk under it

    Homework Statement Consider the pendulum depicted in the adjacent figure: a mass m is attached to non stretching chord of length `. Directly below the pendulum is a circular disc rotating with constant angular velocity w. We attach to the disk a frame whose x-axis is in the plane of the...
  48. G

    Show Energy Equality of Simple Pendulum with Equipartition

    Homework Statement How would one show that the average total energy of a simple pendulum is equal to twice the average kinetic energy of the pendulum? Homework Equations E = T + V = 1/2 ml**2 (θ'**2) + mgl cos(θ) The Attempt at a Solution Maybe use equipartition?
  49. X

    Rotational Motion of a pendulum

    Homework Statement A pendulum is made of a bob dangling from a lightweight string of length ℓ. The bob is pulled sideways so that the string makes an angle θi with respect to the vertical, then released. As it swings down, what is the rotational speed of the bob as a function of the changing...
  50. D

    Time of oscillation of a pendulum

    Homework Statement A rigib poll of length 2L is made into a V shape so that each leg has length L. What is the period of oscillation for small angle. The angle between the legs is 120 degrees Homework Equations 3. The Attempt at a Solution [/B] I tried to calculate the period by imagining a...
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