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[Figure: a block of mass M=490 g on a frictionless table, joined to a rigid support on each side by a spring of constant K=2 N m⁻¹.] A block of mass M=490 g on a frictionless table is connected to two springs of the same constant K=2 N m⁻¹. The block is displaced horizontally through X m and released. The number of complete oscillations it makes in 14π seconds is ______.

Asked in JEE Main 31st Jan 1st Shift 2023 · Spring combinations

Figure: Spring combinations
Answer: 20

Step-by-step solution

The springs are in parallel, so k_eff=2+2=4 N m⁻¹ and ω=√4/(0.49)=2/(0.7)=(20)/7 rad s⁻¹.

T=(2π)/ω=(7π)/(10) s.

Number of oscillations =(14π)/(7π/10)=20.

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