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Question

A mass is suspended from a vertical spring which is executing S.H.M of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is [acceleration due to gravity g = 10m/s2]

A
2πm/s
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B
πm/s
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C
12πm/s
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D
1πm/s
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Solution

The correct option is D 1πm/s

We know that block has maximum speed at equilibrium position.
By applying conservation of mechanical energy at equilibrium position and highest point of oscillation:-

Energy at equilibrium=energy at highest point
12mv2+12kA2=mgA (speed at highest point and elongation in spring is 0.)

And , ω=2πf=10πs1

ω=kmk=mω2

At equilibrium:-
mg=kAA=mgk=gω2
Now:-
12mv2+12mω2A2=mgA

v2=2gAω2A2

v2=2g2ω2g2ω2=g2ω2

v2=102(10π)2=1π2

v=1πm/s

Hence, answer is option-(D).

822622_890633_ans_93bbe53016ac440a97bc1df809057cbe.png

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