Question

A ball and spring system is moving with simple harmonic motion, described by the equation x=4cos(6πt), where x is in cm and t is in seconds. What is the maximum velocity of the ball?

Answer 1

Answer:

V(max)= 24π

Explanation:

Given that

The equation of the SHM given as

x= 4 cos(6πt)

x =Displacement ( in cm)

t=Time ( in sec)

We know that velocity V given as

$V=\dfrac{dx}{dt}$

$\dfrac{dx}{dt} = -4\times 6\pi sin(6\pi t)$

V = -24π sin(6πt)

When  sin(6πt) will become -1 then the velocity of the ball will become maximum.

Therefore the maximum velocity of the ball will be

V(max)= 24π