First slide

Simple hormonic motion

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 ‘a’ , then the block (relative to truck ):

Moderate

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.

Solution

In reference frame fixed to the accelerating truck, we may consider the block as shown in figure. A pseudo force F = m.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 $\frac{2 ma}{K}$ .
But for equilibrium, elongation of this spring should be equal to $\frac{ma}{K}$ . It means block will start to perform oscillations and the amplitude of oscillations will be $\frac{2 ma}{K} - \frac{ma}{K} = \frac{ma}{K}$

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