Answer:
Option D
Explanation:
In SHM , a particle starts from rest, we have
i.e, x=Acosωt, at t=0,x=A
when t=τ then x=A-a .......(i)
when t=2τ , then x=A-3a .......(ii)
On comparing Eqs. (i) and (ii), we get
A−a=Acosωτ
A−3a=Acos2ωτ
As cos2ωt=2cos2τ−1
⇒ A−3aA=2(A−aA)2−1
⇒ A−3aA=2A2+2a2−4Aa−A2A2
A2−3aA=A2+2a2−4Aa
a2=2aA
A=2a
Now, A−a=Acosωτ
⇒ cosωτ=1/2
2πTτ=π3
⇒ T=6π