Question

Suppose that you are pushing a child on a swing, initially at rest, periodically.
(a) Draw a displacement-time graph for the resulting oscillatory motion of the swing.
(b) Is it an example of free or damped or damped forced oscillation?

Answer 1

As we know that,

The swing will work as the simple pendulum, so from the diagram given below.

(a) Let the maximum displacement = a

So, here A is the amplitude,

let the time period of the swing is T,

$\phi=$ phase difference

so $y= a\sin(\dfrac{2\pi}{T}t+\phi)$

(b) The above is am example of Damped force ocsillations.