Question

A spring block system is doing SHM with Amplitude A and angular frequency $\omega$.

At t=T, the particle is at extreme position. Write displacement versus time equation.

• A. $x=Asin\omega t$
• B. $x=A+Asin\omega t$
• C. $x=Acos\omega t$
• D. $x=Asin(\omega t+\frac{\Pi }{2})$

Answer 1

Answer: (C), (D)

$x=Asin(\omega t+\frac{\Pi }{2})$

Generally if particle A at mean position its phase constant is 0 and hence we write x = A sin ωt

But if the particle is at extreme position then the phase constant will be $\frac{\Pi }{2}$ as you can see in the circle diagram.

So equation becomes $x=Asin(\omega t+\frac{\Pi }{2})$

Or $x=Acos\omega t$

Hence both (c) and (d) are correct.