The disperod of a particle varies according to the relation `x=4 (cos pit+ sinpit)`. The amplitude of the particle is.

Options

A. `-4`
B. 4
C. `4sqrt(2)`
D. 8

Answer

C

Explanation

`x=4(cospit+sinpit)`
`=4xxsqrt(2)[(1)/(sqrt(2))cospit+(1)/(sqrt(2))sinpit]`
or `x=4sqrt(2)[sin.(pi)/(4)cospit+cos.(pi)/(4)sinpit]`
`=4sqrt(2)sin(pit+(pi)/(4))`
Hence amplitude = `4sqrt(2)`.