Find the maximum velcoity and maximum acceleration of a particle performing SHM whose displacement is given by x= 2 cos ( 50 t) cm.

Explanation

Data : x = 2 cos ( 50 t) cm
Comparing the given equation with the equation of an SHM.
x = A cos `omegat`
A = 2 cm = 0.02 m and ` omega = 50` rad/s
The magnitude of the maximum velocity.
`V_(max) = omegaA= (50)(0.02) = 1 m//s`
and the magnitude of the maximum accelerations.
` a_(max) = omega^(2)A = omega v_(max) = (50) (1) = 50 m//s^(2)`