A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

Question

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude? (A) 1/2 sec (B) 1/3 sec (C) 1/4 sec (D) 1/6 sec

Tardigrade Admin · Accepted Answer

x=A sin t (2 π/T) ; for x=(A/2) ⇒ (A/2)=A sin (2 π/T) t Solving, t=(T/6) .

Q. A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

1/2 sec

1/3 sec

1/4 sec

1/6 sec

$x = A sin t \frac{2 π}{T};$ for $x = \frac{A}{2} \Rightarrow \frac{A}{2} = A sin \frac{2 π}{T} t$
Solving, $t = \frac{T}{6} .$

Q. A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

1/2 sec

1/3 sec

1/4 sec

1/6 sec

x=AsintT2π​; for x=2A​⇒2A​=AsinT2π​t Solving, t=6T​.

$x = A sin t \frac{2 π}{T};$ for $x = \frac{A}{2} \Rightarrow \frac{A}{2} = A sin \frac{2 π}{T} t$
Solving, $t = \frac{T}{6} .$