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Question

The displacement of a body executing SHM is given by x = A sin (2πt + π3). The first time from t = 0 when the velocity is maximum is:
  1. 0.33 sec
  2. 0.5 sec
  3. 0.25 sec
  4. 0.16 sec

A
0.16 sec
B
0.25 sec
C
0.5 sec
D
0.33 sec
Solution
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The displacement of a body executing SHM is given by:
x=Asin(2πt+π/3)
Velocity, v=dxdt=2πAcos(2πt+π/3)
For maximum velocity,
dvdt=0
4π2Asin(2πt+π/3)=0
sin(2πt+π/3)=sin(nπ)
2πt+π/3=nπ
for n=1
2πt=ππ/3=2π3
t=13=0.33sec
The correct option is A.

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