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  • In the given figure, a body of mass M is  held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body i

In the given figure, a body of mass M is  held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is :
 
Option: 1 \frac{1}{2\pi}\sqrt{\frac{2k}{Mg\; \sin \alpha }}
Option: 2 \frac{1}{2\pi}\sqrt{\frac{k}{2M}}
Option: 3 \frac{1}{2\pi}\sqrt{\frac{2k}{M}}  
Option: 4 \frac{1}{2\pi}\sqrt{\frac{k}{Mg\; \sin \alpha }}

Answers (1)

best_answer

Since the springs are in parallel, so the equivalent spring constant will be

\begin{array}{l} \mathrm{k}_{\mathrm{eq}}=\mathrm{k}_{1}+\mathrm{k}_{2}=2 \mathrm{k} \\ \\ \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{k}_{\mathrm{eq}}}}=2 \pi \sqrt{\frac{\mathrm{M}}{2 \mathrm{k}}} \\ \\ \mathrm{f}=\frac{1}{\mathrm{~T}}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k}}{\mathrm{M}}} \end{array}

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avinash.dongre

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