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Question

A block of mass m is connected to springs as shown in the figure. Find the time period of small oscillations. [All springs are identical]

A
T=2πm3K
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B
T=2πmK
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C
T=2πm2K
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D
T=2π3mK
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Solution

The correct option is A T=2π√m3K Springs (1) and (2) are in parallel combination Thus, K′eq=K1+K2=2K Now, spring (3) and combination of spring (1) and (2) are in parallel again. ∴Keq=K3+K′eq=K+2K=3K Time period of oscillation is given by T=2π√mKeq ⇒T=2π√m3K Thus, option (a) is the correct answer.

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