Question

A pendulum with mass 3 kg is swinging back and forth on a 2.0 m string and a maximum horizontal displacement of 0.1 m from equilibrium. It passes through its equilibrium point going to the right at time t = 0. a) What will its position be at time t = 3.5 seconds? b) What will its velocity be at time t=3.5 seconds?

Answer 1

At t = 0 the pendulum is in equilibrium position of x = 0, Hence we can approximate the pendulum motion with a sine function. Hence we can write,

x0 is the maximum displacement, Substituting values we get,

The velocity can be calculated by taking derivative of the above function, from which we get,

(a) Substituting t = 3.5 for the position equation we get,

(b) Substituting t = 3.5 in the velocity equation we get,