Question

A mass on a frictionless surface is attached to a spring. The spring is compressed from its equilibrium position, B , to point A , a distance x from B . Point C is also a distance x from B, but in the opposite direction. When the mass is released and allowed to oscillated freely, at what point or points is its velocity maximized?

• A. A
• B. B
• C. C
• D. Both A and C
• E. Both A and B

Answer 1

The correct option is B B

When the mass is released , it will undergo SHM , and velocity $v$ in SHM is given by ,

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

where $\omega =$ angular frequency (fixed) ,

$a=$ amplitude (fixed) ,

$y=$ displacement from mean position ,

Now from the above relation we can see that $v$ will be maximum when $y$ is minimum i.e. $y=0$ , which is the mean position of SHM . Therefore velocity is maximum at mean position .