Question:
A particle of mass $3$ kg, attached to a spring with force constant $48$ N/m executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation of the particle, in seconds, is
A particle of mass $3$ kg, attached to a spring with force constant $48$ N/m executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation of the particle, in seconds, is
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Always simplify $\frac{m}{k}$ before taking square root in SHM problems.
Updated On: May 1, 2026
- $\frac{\pi}{4}$
- $\frac{\pi}{2}$
- $2\pi$
- $8\pi$
- $\frac{\pi}{8}$
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The Correct Option is B
Solution and Explanation
Concept:
Time period of SHM: \[ T = 2\pi \sqrt{\frac{m}{k}} \]
Step 1: Substitute values.
\[ m = 3,\quad k = 48 \] \[ T = 2\pi \sqrt{\frac{3}{48}} = 2\pi \sqrt{\frac{1}{16}} \]
Step 2: Simplify.
\[ T = 2\pi \cdot \frac{1}{4} = \frac{\pi}{2} \]
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