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Question

# A particle moves with SHM in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a in same direction then

A
Amplitude of motion is 3a
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B
To!e period of oscillations is 8τ
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C
Amplitude of motion is 4a
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D
To!e period of oscillations is 6τ
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Solution

## The correct option is B To!e period of oscillations is 6τLet A is the amplitude of motion.(A−a)=Acoswt..........(1)&−(3a−A)=Acos2wt⇒A−3a=Acos2wt=A[2cos2wt−1]=2Acos2wt−A⇒2A−2a=2Acos2wt........(2)⇒(A−a)2(2A−3a)=AA2⇒(A2+a2−2Aa)=2A2−3aA⇒2A2+2a2−4Aa=2A2−3aA⇒2a2=aA⇒A=2a∴ form (1)a=2acoswt⇒12=coswt⇒wt=π3⇒2πT.t=π3⇒T=6t∴ Option D is correct.

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