Question

Assertion (A): The phase difference between displacement and velocity in SHM is ${90}^{\circ }$
Reason (R): The displacement is represented by y=A sin$\omega$t and Velocity by V=A$\omega$cos$\omega$t.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is true and R is false
• D. A is false and R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

At mean displacement is Zero but velocity is maximum At extreme position displacement is maximum but velocity is Zero.
Thus displacement can be represented by
$y$= $Asinwt$
$V=\frac{dy}{dt}$
$=Awcoswt=Awsin(wt+\frac{\pi }{2})$
Thus phase difference is $\frac{\pi }{2}$