If two particles performing SHM, are given by,
`x_(1)=10 sin[3pi t +(pi//4)] and `
`x_(2)=5[sin 3pi t +sqrt(3) cos 3 pi t]`
then the ratio of their amplitudes is

Options

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

Answer

B

Explanation

Given that
`x_(2)=5sin 3pi t +5 sqrt(3)cos 3 pi t`
`=5sin 3pi t + 5 sqrt(3) sin (3pi t-(pi)/(2))`
So, the amplitude `R_(2)` is given by
`R_(2)=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)+A_(2)cos(alpha_(1)-alpha_(2)))`
`=sqrt(25+25xx3+2xx5xx5sqrt(3)xxcos(pi//2))`
`=sqrt(25+75)=sqrt(100)=10 cm`
And `x_(1)=10 sin(3pi t+(pi)/(4))`
`therefore R_(1)=10 cm`
`therefore (R_(1))/(R_(2))=(10)/(10)=(1)/(1)`