Ncert Exercises & Solutions

A spring with one end attached to a mass and the other to rigid support is stretched and released. Then:

(a) Magnitude of acceleration, when just released is maximum
(b) Magnitude of acceleration, when at the equilibrium position, is maximum
(c) Speed is maximum when mass is at the equilibrium position
(d) Magnitude of displacement is always maximum whenever speed is minimum

Choose the correct option:

1. (b, c)

2. (a, c)

3. (b, d)

4. (a, c, d)

(2) Hint: The spring force is directly proportional to the displacement.

Step 1: Find the acceleration of the mass.

When spring is stretched by x, restoring force will be F = - kx
Potential enerav.of the stretched spring $= PE = \frac{1}{2} {kx}^{2}$

The restoring force is central hence when a particle released it will execute SHM about the equilibrium position.

$\begin{array}{ll} Acceleration will be & a = \frac{F}{m} \pm \frac{- Kx}{m} \\ At equilibrium position, & x = 0 \Rightarrow a = 0 \\ Hence, when just released & x = x_{\max} \end{array}$

Step 2: Find the speed at the mean position.

At equilibrium whole PE will be converted to KE hence, KE will be maximum and hence, speed will be maximum.

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