Question

When a spring-mass system vibrates with simple harmonic motion, the mass in motion reaches its maximum velocity:

• A. when its acceleration is greatest
• B. when its acceleration is least.
• C. once during one oscillation.
• D. when it is as its maximum displacement from equilibrium.
• E. when it experiences maximum force.

Answer 1

The correct option is B when its acceleration is least.

Velocity in SHM is given by ,

$v=\omega \sqrt{a^2-y^2}$ ,

where $\omega =$ angular velocity ,

$a=$ amplitude ,

$y=$ displacement from mean position ,

velocity $v$ will be maximum when RHS of this relation is maximum , this is maximum when $y$ is minimum i.e.$y=0$ ,

now acceleration in SHM is given by ,

$A=-{\omega }^{2}y$ ,

therefore acceleration at $y=0$ will be ,

$A=0$ ,

it implies that velocity is maximum when acceleration is least .