Question

An object exhibits SHM with an angular frequency w = 4.0 s-1 and is released from its maximum displacement of A = 0.50 m at t = 0 s. At what time, t, does it reach its maximum speed?

Answer 1

Explanation:

It is given that,

Angular frequency, $\omega=4\ s^{-1}$

Maximum displacement, A = 0.5 m at t = 0 s

We need to find the time at which it reaches its maximum speed. Firstly, we will find the maximum velocity of the object that is exhibiting SHM.

$v_{max}=A\times \omega$

$v_{max}=0.5\times 4$

$v_{max}=2\ m/s$............(1)

Acceleration of the object, $a=\omega^2A$

$a=4^2\times 0.5$

$a=8\ m/s^2$...............(2)

Using first equation of motion we can calculate the time taken to reach maximum speed.

$v=u+at$

$t=\dfrac{v-u}{a}$

$t=\dfrac{2-0}{8}$

t = 0.25 s

So, the object will take 0.25 seconds to reach its maximum speed. Hence, this is the required solution.