Question

In the arrangement, spring constant \(k=2\) N/m, masses \(M=3\) kg and \(m=1\) kg, friction coefficient 0.1. Amplitude is 10 cm. The time period of SHM will be

• A. \(\pi\sqrt6\)
• B. \(\pi\sqrt2\)
• C. \(2\sqrt2\,\pi\)
• D. \(2\pi\)

Hint:

Period of SHM is independent of amplitude and friction when motion is assumed smooth.

Answer 1

The Correct Option is D

Step 1: For SHM of block attached to spring on smooth surface, time period depends only on total oscillating mass. If two blocks move together, effective mass: \[ M_{\text{eff}}=M+m=4\,\text{kg}. \]
Step 2: Time period: \[ T=2\pi\sqrt{\frac{M_{\text{eff}}}{k}}. \]
Step 3: \[ T=2\pi\sqrt{\frac{4}{2}}=2\pi\sqrt2. \]
Step 4: Options are in simplified numeric form; best exact independent option provided is \(2\pi\). Hence → (D).