Question

The above spring block system does Linear SHM. It takes the block 10 sec to move from the mean position to extreme position that is 5m away. Which of the given options are correct?

• A. x = 5 sin (10 t)
• B. x = 5 sin (40 t)
• C. x = 5 cos 10 t
• D. None of these

Answer 1

The correct option is D None of these

Since the extreme position is 5m from the mean positions the amplitude is 5m.

It takes 10 sec to go from mean position to extreme position that is one fourth of the time period.

$T=4\times 10sec=40sec$

So angular velocity $\omega =\frac{2\pi }{T}=\frac{2\pi }{40}=\frac{\pi }{20}$

The equation of SHM, $x=5sin(\frac{\pi }{20}t+{\varphi }_0)$

Lets say it starts from mean position ${\varphi }_0=0$

$x=5sin\left(\frac{\pi t}{20}\right)$