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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 equation given represent simple hormonic motion along the X-ray with amplitudes `A_(1) = 2.0 cm and A_(2) = 2.0 cm`. The phase different between the two simple harmonic motion is `pi//3`. The resultant imple harmonic motion will have an amplitude. A given by
`A = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1) , A_(2) cosdelta)`
`= sqrt ((2.0 cm)^(2) + (2.0 cm)^(2) + 2 (2.0 cm)^(2) cos) (pi)/(3) = 3.5 cm`
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