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
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
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Period of SHM is independent of amplitude and friction when motion is assumed smooth.
Updated On: Jan 9, 2026
- \(\pi\sqrt6\)
- \(\pi\sqrt2\)
- \(2\sqrt2\,\pi\)
- \(2\pi\)
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The Correct Option is D
Solution and Explanation
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).
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).
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