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Question

Two springs with negligible masses and force constant of K1=200Nm1 and K2=160Nm1 are attached to the block of mass m=10 kg as shown in the figure.Initially the block is at rest ,at the equilibrium position in which both springs are neither stretched nor compressed.At time t=0, a sharp impulse of 50 Ns is given to the block with a hammer
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A
Period of oscillations for the mass m is π6s
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B
Maximum velocity of the mass m during its oscillation is 10 ms1
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C
Data are insufficient to determine maximum velocity
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D
Amplitude of oscillation is 0.83 m
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Solution

The correct option is A Period of oscillations for the mass m is π6s
Keff=K1+K2
Keff=(200+160)Nm1=360 Nm1
F=Keffx=50 N, means, Ampletude of SHM =x=50360 m
T=2πmKeff=2π10360=π3
ω=2πT=2π(π3)=6 rad/sec
vmax=ωx(amplitude)=6×536=56 ms1
only"A" is correct.

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