The time period of simple harmonic motion of mass M in the given figure is where the value of is

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Solution

Q.
The time period of simple harmonic motion of mass M in the given figure is $π \sqrt{\frac{α M}{5 k}},$ where the value of $α$ is ________ . [2024]

Ans.
(12)

$k_{eq} = \frac{2 k \cdot k}{3 k} + k = \frac{5 k}{3}$

Angular frequency of oscillation $(ω) = \sqrt{\frac{k_{eq}}{m}}$

$(ω) = \sqrt{\frac{5 k}{3 m}}$

Period of oscillation $(τ) = \frac{2 π}{ω} = 2 π \sqrt{\frac{3 m}{5 k}}$

$= π \sqrt{\frac{12 m}{5 k}}$

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