The velocity of a particle executing simple harmonic motion along x -axis is described as v^2 = 50 - x^2 , where x represents displacement. If the time period of motion is x 7 s, the value of x is _____.

Step-by-step solution

The given equation is v^2 = 50 - x^2 Differentiating with respect to x : 2v dv dx = -2x v dv dx = -x Since acceleration a = v dv dx , we get: a = -x Comparing this with the standard equation of SHM a = - ^2 x , we get: ^2 = 1 = 1 rad/s The time period of the motion is given by: T = 2 = 2 Taking = 22 7 , we get: T = 2 22 7 = 44 7 s Given that the time period is x 7 s, comparing the two gives: x = 44 Answer: 44