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If two particles performing SHM, are giv...

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

A

`2 : 1`

B

`1 : 1`

C

`1 : 2`

D

`1 : sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y_(2)=5sin3pit+5sqrt(3)cos3pit`
`R_(1)=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosalpha_(1)-alpha_(2))`
`=sqrt(25+25xx3+25xxsqrt(3)xxcos(pi//2))`
`=sqrt(25+75)=sqrt(100)`
`R_(1)=10cmR_(2)=10cm`
`(R_(1))/(R_(2))=(10)/(10)=(1)/(1)`
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