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Two simple harmonic motions are represen...

Two simple harmonic motions are represented by the equations
`y_(1) = 10 sin(3pit + pi//4) and y_(2) = 5(sin 3pit + sqrt(3)cos 3pit)` their amplitude are in the ratio of ………… .

A

`sqrt(3)`

B

`1//sqrt(3)`

C

2

D

`1//6`

Text Solution

Verified by Experts

The correct Answer is:
C
`x_(1)=10sin(3pit+(pi)/(4))`
and `x_(2)=5(3sin3pit+sqrt(3)cos3pit)`
`=10sqrt(3)((sqrt(3))/(2)sin3pit+(1)/(2)cos3pit)`
or `x_(2)=10sqrt(3)sin(3pit+(pi)/(6))`
`therefore` Ratio of their amplitudes = `(10)/(10sqrt(3))=(1)/(sqrt(3))`
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