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A particle executes simple harmonic moti...

A particle executes simple harmonic motion represented by displacement function as
`x(t)=A sin(omegat+phi)`
If the position and velocity of the particle at t = 0 s are 2 cm and `2omega" cm s"^(-1)` respectively, then its amplitude is `xsqrt(2)` cm where the value of x is _________.

Text Solution

Verified by Experts

The correct Answer is:
2
` 2 = A sin (0 + phi)`
`rArr sin phi = (2)/(A)`
`rArr cos phi = sqrt( 1 - (4)/( A^(2))) = sqrt((A^(2) - 4)/( A^(2)))`
`V = (dx)/( dt)`
`V = A omega cos ( omega t + phi)`
`rArr 2 omega = A omega cos (0 + phi)`
`rArr 2 = A cos phi `
`rArr A = (2)/( cos phi)` . . . (i)
`rArr A = (2)/( sqrt(( A^(2) - 4)/( A^(2))))`
`rArr a = (2 A)/( sqrt( A^(2) - 4))`
`rArr sqrt(A^(2) - 4) = 2 `
`rArr A + pm sqrt(8) = pm 2 sqrt( 2)`
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