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A mass attached to a spring is free to oscillate, with angular velocity omega in a horizontal plane without friction or damping. It is pulled to a distance x_0 and pushed towards the centre with a velocity v_0 at time t=0. Determine the amplitude of the resulting oscillations in terms of the parameters omega, x_0 and v_0 |
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Answer» Solution :x= A `cos (OMEGA x + theta) `, velocity , `(DX)/(dt) =- A omega sin(OMEGAT + theta)` When t=0 , `x=x_0 and (dx)/(dt) = -v_0` `THEREFORE x_0 = A cos theta ""……..(i)` `-v_0 = - A omega theta ` (or) ` A sin theta = v_0//omega ""......(ii)` Squaring and adding (i) and (ii) , we get , `A^2 (sin^2 theta + cos^2 theta) = (v_0^2 //omega^2) + x_0^2 , A= [v_0^2 .//omega^2 + x_0^2J^(1//2)]` |
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