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A particle is subjected to two simple ha...

A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of `45^@` with the X-axis. The two motions are given by
`x=x_0 sinomegat` and `s=s_0 sin omegat`.
find the amplitude of the resultant motion.

Text Solution

Verified by Experts

The correct Answer is:
A, B
The particle is subjected to two simple harmonic motions represented by
`x=x_0sin2t`
`s=s_0sinwt`
and angle between two motion
`theta=45^@`
Resultant motions will be given by
`R=sqrt(x^2+s^2+2xs.cos45^@)`
`=sqrt({x_0^2sin^2 wt+s_0^2sin^2wt+2x_0s_0sin^2omegat)1/sqrt2)})`
`=[x_0^2+s_0^2+sqrt(2x_0s_0)]^(1/2) sin omegat`
Resultant amplitude
`[x_0^2+s_0^2+sqrt(2x_0s_0)]^(1/2)`
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