The displacement of a particle varies according to the relation `y = 4(cos pi t + sin pi t)`. The amplitude of the particle is

Options

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

Answer

D

Explanation

`x = 4(cos pi t + sin pi t)`
`= 4 sqrt(2) [(1)/(sqrt(2)) cos pi t + (1)/(sqrt(2)) sin pi t]`
`= 4 sqrt(2) [sin(pi)/(4) cos pi t + cos (pi)/(4)sin pi t]`
`4 sqrt(2) sin (pi t + (pi)/(4))`
Standard equation of displacement is
`x = a sin ( omega t + phi)`
Comparing the given equation with standerd equation
`a = 4 sqrt(2)`