Question

An object of mass $m$ is performing simple harmonic motion on a smooth horizontal surface as shown in figure. Just as the oscillating object reaches its extreme position, another object of mass $2m$ is dropped on to it gently, which sticks to it. Mark out the correct statement(s) for the given situation.

• A. Amplitude of oscillation remains unchanged
• B. Time period of oscillation remains unchanged
• C. The total mechanical energy of the system does not change
• D. The maximum speed of the oscillating object changes

Answer 1

Answer: (A), (C), (D)

The maximum speed of the oscillating object changes

Since total mass changes, time period $T$ changes.
Initially $T_i=2\pi \sqrt{\frac{m}{K}}$
After mass is added, $T_f=2\pi \sqrt{\frac{3m}{K}}$
Amplitude $A$ remains the same as the body of mass $2m$ is attached when the oscillating body is at its extreme position
Total energy does not change as at extreme position, the total energy is in the form of potential energy which is independent of mass.
Maximum velocity $V_{\text{max}}=\pm A\omega$ (at mean position)
Although $A$ is same, $T$ changes, hence $\omega$ changes i.e $V_{\text{max}}$ also changes.
Therefore, options (a), (c) and (d) are correct.