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Two simple harmonic motions are represen...

Two simple harmonic motions are represented by the equations:
`x_(1)=5sin(2pit+(pi)/(4)),x^(2)=5sqrt(2)(sin2pit+cos2pit)`
What is the ratio of their amplitudes?

Text Solution

Verified by Experts

`x_(1)=5sin(2pit+(pi)/(4))" "[therefore A_(1)=5]`
`x_(2)=5sqrt(2)(sin2pit+cos2pit)`
`=10sin(sin2pitcos.(pi)/(4)+cos2pitsin.(pi)/(4))`
`x_(2)=10sin(2pit+(pi)/(4))" "[therefore A_(2)=10]`
Hence, `(A_(1))/(A_(2))=(5)/(10)=1:2`
`A_(1):A_(2)=1:2`
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