The displacement of a particle is represented by the equation
`y=0.4{"cos"^(2)((pi t)/(2))-"sin"^(2)((pit)/(2))}`metre
The motion of the particle is

Options

A. a S.H.M. with amplitude 0.8 m
B. oscillatory but not S.H.M.
C. a S.H.M. with amplitude 0.4 m
D. a S.H.M. with amplitude `0.4sqrt(2)m`

Answer

C

Explanation

`y=0.4 {"cos"^(2)((pi t)/(2))-"sin"^(2)((pi t)/(2))}m`
`because "cos" 2 theta ="cos"^(2)theta-"sin"^(2)theta`
`therefore "cos"^(2)((pi t)/(2))-"sin"^(2)((pi t)/(2))="cos"(2(pit)/(2))="cos" (pi t)`
`therefore` The given equation is `y=0.4 "cos" (pi t)`
Comparing with `y=A "cos" (omega t)` we find that the motion of the particle is a S.H.M. of amplitude 0.4 m.