A mass m is attached to two springs as shown in figure. The spring constants of the two springs are K₁ and K₂. For the frictionless surface, the time period of oscillation of mass m is: Image
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Question

A mass m is attached to two springs as shown in figure. The spring constants of the two springs are K₁ and K₂. For the frictionless surface, the time period of oscillation of mass m is: Image

G1 Physics · Accepted Answer

The two springs act simultaneously on the mass, so their restoring forces add. Effective spring constant: K(eff) = K₁ + K₂ For SHM: T = 2π√[m/K(eff)] Therefore, T = 2π√[m/(K₁ + K₂)] Hence option D follows.