AP EAMCET · PHYSICS · Oscillations

One end of a spring of force constant $k$ is fixed to a vertical wall and the other to a block of mass $m$ resting on a smooth horizontal surface. There is another wall at a distance $x_{0}$ , from the block. The spring is then compressed by $2 x_{0}$ and released. The time taken by the block to strike the other wall is

A $\frac{1}{6} π \sqrt{\frac{m}{k}}$
B $\sqrt{\frac{m}{k}}$
C $\frac{2 π}{3} \sqrt{\frac{m}{k}}$
D $\frac{π}{4} \sqrt{\frac{m}{k}}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{2 π}{3} \sqrt{\frac{m}{k}}$

Step-by-step Solution

Detailed explanation

Given, Maximum compressionA=2x0 Distance of block from wallx=x0 Mass of block=m kg Since initially block is at extreme position, its equation will be- x=Asin ωt+π2=2x0 cos ωt When block hit the wall, its position will be x=-x0 Put this value in…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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