The time period and the amplitude of a simple pendulum are 4 seconds and 0.20 meter respectively. If the displacement is 0.1 meter at time t=0, the equation on its displacement is represented by :-

Explanation

The general equation of SHM is y = a sin `(omega t + phi)`
At t = 0, y = 0.1 m and a = 0.2 m
`rArr 0.1 = 0.2 sin (omega xx 0 + phi)`
`rArr (1)/(2) = sin (phi) rArr phi = (pi)/(6)`
Next, `omega = (2pi)/(T) rArr omega = (2pi)/(4) = 0.5 pi`
Substituting values of a and `phi` in the general SHM equation `therefore" " y = 0.2 (m) sin ((pit)/(2) + (pi)/(6))`