A particle moves along the `X`-axis according to to the law `S=a sin^(2)(omegat-pi//4)`
The amplitude of the oscillation is

Options

A. `(a)/(2)`
B. `(A)/(4)`
C. `(A)/(5)`
D. A

Answer

A

Explanation

The equation of motion `x=A "sin"^(2)(omega t- (pi)/(4))`
This can be expressed as
`x=(A)/(2)[1-"cos"{2(omega t-(pi)/(4))}]`
`therefore` The amplitude is `(A)/(2)`
Proof :
`"cos" 2 theta="cos"^(2)theta-"sin"^(2)theta="cos"^(2)theta+"sin"^(2)theta-2"sin"^(2)theta`
`therefore "cos" 2 theta=1-2 "sin"^(2)theta`
`therefore "sin"^(2)theta=((1-"cos" 2theta)/(2))`