Question:
A mass \( m \) hanging from a spring is doing simple harmonic motion with frequency \( f \). If the mass is increased by 4 times, then frequency will be:
A mass \( m \) hanging from a spring is doing simple harmonic motion with frequency \( f \). If the mass is increased by 4 times, then frequency will be:
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Frequency in SHM is inversely proportional to square root of mass.
Updated On: Apr 16, 2026
- \(2f\)
- \( \frac{f}{2} \)
- \(4f\)
- \( \frac{f}{4} \)
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The Correct Option is B
Solution and Explanation
Concept:
Frequency of SHM:
\[
f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}
\]
Step 1: Relation with mass.
\[ f \propto \frac{1}{\sqrt{m}} \]
Step 2: Mass increased 4 times.
\[ f' = \frac{f}{\sqrt{4}} = \frac{f}{2} \]
Step 1: Relation with mass.
\[ f \propto \frac{1}{\sqrt{m}} \]
Step 2: Mass increased 4 times.
\[ f' = \frac{f}{\sqrt{4}} = \frac{f}{2} \]
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