AP EAMCET · PHYSICS · Oscillations
On a smooth inclined plane, a block of mass \(M\) is fixed to two rigid supports using two springs, as shown in the figure. If each spring has spring constant \(k\), then the period of oscillation of the block is
(Neglect the masses of the springs)
- A \(2 \pi\left(\frac{\mathrm{M}}{2 \mathrm{k}}\right)^{1 / 2}\)
- B \(2 \pi\left(\frac{2 \mathrm{M}}{\mathrm{k}}\right)^{1 / 2}\)
- C \(2 \pi\left(\frac{\mathrm{Mg} \sin \theta}{2 \mathrm{k}}\right)^{1 / 2}\)
- D \(2 \pi\left(\frac{2 \mathrm{Mg}}{\mathrm{k}}\right)^{1 / 2}\)
Answer & Solution
Correct Answer
(A) \(2 \pi\left(\frac{\mathrm{M}}{2 \mathrm{k}}\right)^{1 / 2}\)
Step-by-step Solution
Detailed explanation
\(k_{eff} = k + k = 2k\) \(T = 2\pi\sqrt{\frac{M}{k_{eff}}}\) \(T = 2\pi\left(\frac{M}{2k}\right)^{1/2}\)
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