Two S.H.M. s are represented by the equation `x_(1)=3"sin" (2pi t+(pi)/(4)) " and " x_(2)=3sqrt(2)["sin" (2pi t)+"cos"(2pi t)]`
What is the ratio of the amplitudes of `x_(1) " and " x_(2)` ?

Options

A. `2 :1`
B. `1 : 2`
C. `1 : 3`
D. `sqrt(3) : 1`

Answer

B

Explanation

`x_(1)=3 "sin" (2pi t+(pi)/(4))`
`x_(2)=3sqrt(2)["sin"(2pi t)+"cos"(2pi t)]`
`=3sqrt(2)xxsqrt(2)["sin"(2pi t)(1)/(sqrt(2))+"cos" (2pi t)(1)/(sqrt(2))]`
But `(1)/(sqrt(2))="sin" (pi)/(4)="cos" (pi)/(4)`
`therefore x_(2)=6 "sin" (2pi t+(pi)/(4))`
`therefore` From (1) and (2),
Amplitude ratio of `x_(1) and x_(2)=(3)/(6)=(1)/(2)`