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Question

A block of mass 100 g attached to a spring of spring constant 100 N/m. The block is moved to compress the spring by 10 cm and then released on a frictionless floor as shown below. If the collisions with the wall in the front are elastic in nature, then the time period of the motion is


A
0.2 s
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B
0.1 s
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C
0.15 s
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D
0.132 s
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Solution

The correct option is D 0.132 s
Given,
Mass of block ((m)=100 g
Spring constant (K)=100 N/m
Mass compression (A)=10 cm
Separation between wall and block (x)=5 cm
Time period (T)=2πmK
=2×3.14×0.1100
=0.198 s
From, x=Asinωt
time taken for particle to reach from mean position to the wall is
5=10sinωt
sinωt=12 (or) ωt=π6
t=T/12
Now time of oscillation is half of the time period + timetaken for particle to reach the wall from mean position and from wall to mean position
T2+2t
T2+T6=2T3=23×0.198=0.132 s

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