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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 givne represent simple harmonic motions along X-axis with ampitudes `A_1=2.0cm and A_2=2.0`. The phase difference between the two simple harmonic motion is `pi/3`. The resultant simple harmonic motion will have an amplitude A given A
`A=sqrt(A_1^2+A_2^2+2A_1A_2cosdelta)`
`=sqrt((2.0cm)^2+(2.0cm)^2+2(2.0cm)^2cospi/3))`
`=3.5cm`
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