A mass m is attached to two springs as shown in figure. The spring constants of two springs are K₁ and K₂. For the frictionless surface, the time period of oscillation of mass m is: (a) 2π√((m)/(K₁+K₂)) (b) 2π√((m)/(K₁-K₂)) (c) 1/2π√((K₁+K₂)/(m)) (d) 1/2π√((K₁-K₂)/(m))

Answer: (a). Displacing m stretches one spring and compresses the other; both restoring forces act together, so they are in parallel. keff = K₁ + K₂ T = 2π√((m)/(K₁+K₂)), so the answer is (a).

A mass m is attached to two springs as shown in figure. The spring… | JEE Main 2023 (6 Apr, Shift 1)

Q48JEE Main 2023 · 6 APR · SHIFT 1Easy

Spring Systems

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2$ . For the frictionless surface, the time period of oscillation of mass $m$ is:

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Answer: (a)

Displacing $m$ stretches one spring and compresses the other; both restoring forces act together, so they are in parallel.
$k_{eff} = K_1 + K_2$
$T = 2\pi\sqrt{\frac{m}{K_1+K_2}}$ , so the answer is (a).

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