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Question

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

A
12
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B
12
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C
2
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D
2+1
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Solution

The correct option is D 2+1
Given that,
Time period of the particle (T)=8 s
As the particle starts from mean position, upto t=T4=2 s, motion of particle is in same direction, hence distance is same as displacement.

When t=1 sec, y1=Asin(2πTt1)
y1=Asin[2π8(1)]=A2 (1)
When t=2 sec
y2=Asin[2π8(2)]=A (2)
d1std2nd=y1y2y1=(A2)AA2=1(21)×(2+1)(2+1)
d1std2nd=2+1
Hence, the correct option is (d).

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