A particle is executing simple harmonic motion of amplitude 5 cm and period 6 s. How long will it take to move from one end of its path on one side of mean position to a position 2.5 cm on the same side of the mean position ?

Options

A. 1 s
B. 1.5 s
C. 3 s
D. 3.5 s

Answer

A

Explanation

The equation of simple harmonic motion when time is computed from the instant it is in extreme position is
`x=Acosomegat=Acos.(2pi)/(T)t`
Here, `A=5cm,T=6s therefore x=5cos.(2pi)/(6)t=5cos.(pi)/(3)t`
When `x=2.5cm, 2.5=5cos.(pi)/(3)t or cos.(pi)/(3)t=(1)/(2)`
or `(pi)/(3)t=cos^(-1)((1)/(2))=(pi)/(3)ort=1s`