Question

Suppose that you are pushing a child on a swing, initially at rest, periodically. Draw a displacement-time graph for the resulting oscillatory motion of the swing

Answer 1

As we know that,

The swing will work as the simple pendulum, so as per the below diagram

Let the maximum displacement = a

So, here A is the amplitude,

let the time period of the swing is T,

$\phi=$ phase difference

so $y= a\sin(\dfrac{2\pi}{T}t+\phi)$