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Question: Answered & Verified by Expert
In arrangement given in figure, if the block of mass $m$ is displaced, the frequency is given by

PhysicsOscillationsJEE Main
Options:
  • A $n=\frac{1}{2 \pi} \sqrt{\left(\frac{k_1-k_2}{m}\right)}$
  • B $n=\frac{1}{2 \pi} \sqrt{\left(\frac{k_1+k_2}{m}\right)}$
  • C $n=\frac{1}{2 \pi} \sqrt{\left(\frac{m}{k_1+k_2}\right)}$
  • D $n=\frac{1}{2 \pi} \sqrt{\left(\frac{m}{k_1-k_2}\right)}$
Solution:
1319 Upvotes Verified Answer
The correct answer is: $n=\frac{1}{2 \pi} \sqrt{\left(\frac{k_1+k_2}{m}\right)}$
With respect to the block the springs are connected in parallel combination.
$\therefore$ Combined stiffness $k=k_1+k_2$ and $n=\frac{1}{2 \pi} \sqrt{\frac{k_1+k_2}{m}}$

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