Question

A particle is oscillating according to the equation $X=7\cos 0.5\pi t$, where $T$ is in second. The point moves from the position of equilibrium to maximum displacement in time.

• A. 4.0 sec
• B. 2.0 sec
• C. 1.0 sec
• D. 0.5 sec

Answer 1

The correct option is C 1.0 sec

A particle is oscillating according to the equation $X=7cos0.5\pi t$.---------(i)

We know that ,

$X=Acos\omega t$

$T=\frac{2\pi }{\omega }$ \\ Where $T$ is the total time taken

On comparing eq (i) we get $\omega =0.5\pi$

Or, $T=\frac{2\pi }{0.5\pi }$

Or, $T=4$ sec

To move from the position of equilibrium to maximum displacement time needed $=\frac{T}{4}=1sec$