Assuming no friction, describe the motion of a simple pendulum released from rest at t=0 at amplitude A? Provide information about its speed and position at characteristic times during one period. [The 1D equation of motion is described by a cosine]

The displacement of the bob of mass m is given by the equation x(t)=A cos(w*t), with no phase offset as given by the boundary conditions (zero speed at t=0). By differentiating this equation twice the first and second derivatives of displacement, i.e. speed and acceleration as a function of displacement can be obtained. By finding maxima of these quantities by looking at peaks of higher order derivatives, one can find the times t at which speed and acceleration are maximised and plot the graphs for one period.
Either we can treat this mathematically or provide physical insight into what should happen to the pendulum. As the pendulum is released from rest, the initial speed is zero. Due to the tangential component of the gravitational force, the bob of mass m is accelerated until it reaches a maximum speed at zero height. As the mass continues to move due to inertia and the gravitational force acting now opposite to its motion, it will slow down again and reach the same height as initially (assuming no air resistance etc.).

Answered by Stefan A. Physics tutor

1445 Views

See similar Physics GCSE tutors

Related Physics GCSE answers

All answers ▸

A jug containing 0.250 kg of liquid is put into a refrigerator. Its temperature decreased from 20°C to 15°C. The amount of energy transferred from the liquid was 5,250 J. Calculate the specific heat capacity of the liquid.


An apple is suspended a string and a spring in parallel. When the string is cut, the apple falls, and the spring stretches and contracts repeatedly as the apple bounces. Describe the energy conversions that occur during this process.


What is the wavelength of a wave travelling at 20ms^-1 with a time period of 0.2s


What is the difference between a transverse and longitudinal wave?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences