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Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsOscillations2 Marks
Question
Answer the following questions:Time period of a particle in SHM depends on the force constant k and mass m of the particle: $\text{T}=2\pi\sqrt{\frac{\text{m}}{\text{k}}}.$ A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
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Answer

The time period of a simple pendulum, $\text{T}=2\pi\sqrt{\frac{\text{m}}{\text{k}}}$For a simple pendulum, k is expressed in terms of mass m, as:
$\text{k}\propto\text{m}$
$\frac{\text{m}}{\text{k}}=\text{Constant}$
Hence, the time period T, of a simple pendulum is independent of the mass of the bob.

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