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Question

# The period of a particle in linear SHM is 8 s. At t=0 it is at the mean position. Find the ratio of distance traveled by it in 1st second and 2nd second

A
3.2:1
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B
2.4:1
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C
1.6:1
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D
4.2:1
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Solution

## The correct option is A 2.4:1 Since particle is starting from mean position, the equation of displacement is x=Asinωt, where A is amplitude of oscillation.Now, ω=2πT=2π8=π4rad/s. Distance travelled in 1 second= x1=Asinωt=A(sinπ4×1)=A√2Distance travelled in 2 seconds=x2=Asinωt=A(sinπ4×2)=ADistance travelled in 2nd second=x2−x1=A−A√2=A(√2−1√2)Taking ratio, we get Answer=x1x2−x1=A√2A(√2−1√2)=√2+1=2.4:1Option B is correct.

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