A particle executes S.H.M. of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position ?

Options

A. 0.5 s
B. 1 s
C. 1.5 s
D. 2 s

Answer

A

Explanation

In order of find the time taken by the particlee from -12.5 cm to +12.5 cm on either side of mean position, we will find the time taken by parrticle to go from x=-12.5 cm to x=0 and to go from x=0 to x=+12.5 cm.
let the equation of motion be `x=Asinomegat`
First, the particle moves from
`x=-12.5cm` to x=0
`therefore12.5=25sinomegat" "(becauseA=25cm)`
`implies(1)/(2)sinomegatimpliesomegat=(pi)/(6)`
`thereforet=(pi)/(6omega)`
`therefore`Total time taken from x=-12.5cm to=12.5 cm
`t=(pi)/(6omega)+(pi)/(6omega)=(pi)/(3omega)`
`=(pi)/(3((2pi)/(T)))=(T)/(6)=(3)/(6)=0.5s`