Question

One end of an ideal spring is connected with a smooth block with the other end with rear wall of driving cabin of a truck as shown in figure. Initially, the system is at rest. If truck starts to accelerate with a constant acceleration then the block (relative to truck):

• A. will remain stationary.
• B. will start oscillating with constant amplitude.
• C. will start oscillating with increasing amplitude.
• D. moves such that length of the spring first increases and then becomes constant.

Answer 1

Answer: (B)

In reference frame fixed to the accelerating truck, we may consider the block as shown in figure. A pseudo force $F= m \cdot a$ is acting on the block towards left. Since magnitude of the force is constant, therefore, maximum elongation of the spring will be equal to $\frac{2 m a}{K}$

But for equilibrium, elongation of this spring should be equal to $\frac{m a}{K}$. It means block will start to perform oscillations and the amplitude of oscillations will be equal to $\frac{2 m a}{K}-\frac{m a}{K}=\frac{m a}{K}$.