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Find the amplitude of the simple harmoni...

Find the amplitude of the simple harmonic motion obtasined by combining the motions
`x_1=(2.0 cm) sinomegat`
` and x_2=(2.0cm)sin(omegat+pi/3)`

Text Solution

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The two equations given represent simple harmonic motions along `X-`axis with amplitudes `A_(1) = 2.0 cm` and `A_(2) = 2.0 cm`. The phase difference between the two simple harmonic motions is `pi//3`. The resultant simple harmonic motion will have an amplittude A given by
`A = sqrt(A_(1)^(2) - A_(2)^(2) + 2A_(1)A_(2)cosdelta) = sqrt((2.0cm)^(2) + (2.0cm)^(2) + 2(2.0cm)^(2) + cos'(pi)/(3)) = 3.5 cm`
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