For a simple pendulum, the time period is 3 s and has a maximum displacement of 5 cm on either side of its mean position. If at the beginning of the motion, the pendulum is at maximum displacement from its mean position, towards its right, then derive the displacement equation of the pendulum.

Explanation

The displacement in S.H.M. is given by
`y = A sin (omegat + delta)`
Here T = 3 s, A = 5 cm
`therefore omega = (2pi)/(T) = (2pi)/(3) ` rad/s
`rArr y = 5 sin((2pi)/(3)t + delta)`
Now, at `t = 0, y = 5 ` cm
So, `5 = 5 sin((2pi)/(3) xx 0 + delta)`
`= sin delta = 1 or delta = pi//2`
So, the displacement equation of the pendulum is
` y = 5 sin((2pi)/(3)+ pi//2)`