A spring with one end attached to a mass and the other to a rigid support is stretched and released.a) magnitude of acceleration, when just released is maximumb) magnitude of acceleration, when at equilibrium position is maximumc) speed is maximum when mass is at equilibrium positiond) magnitude of displacement is always maximum whenever speed is minimum

The correct answer is the option:

(a) Magnitude of acceleration, when just released is maximum.

(c) Speed is maximum when mass is at the equilibrium position.

Explanation: Let us consider a spring lying on a frictionless table. Let k be the spring constant, viz., attached to a mass ‘m’ at one end and the other end is fixed at right support.

Now let us stretch the spring to a displacement x by force F,

Now, P.E. at

Since restoring force is proportional to x, Simple Harmonic Motion is executed here.

Therefore,

Or

&

Thus, when spring is released, the magnitude will be maximum. Hence, opt(a) is verified here.

At x = 0, the speed of mass is maximum.

Hence opt (c) is also verified.

At x = 0, the magnitude of a = 0.

The speed of mass may or may not be zero when it is at its maximum displacement.

Hence, opt (d) is also discarded here.