Oscillations Question 8
Question 8 - 2024 (31 Jan Shift 2)
The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is
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Answer: (12)
Solution:
$k _{eq}=\frac{2 k \cdot k}{3 k}+k=\frac{5 k}{3}$
Angular frequency of oscillation $(\omega)=\sqrt{\frac{k _{eq}}{m}}$
$(\omega)=\sqrt{\frac{5 k}{3 m}}$
Period of oscillation $(\tau)=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{3 m}{5 k}}$
$=\pi \sqrt{\frac{12 m}{5 k}}$
