A particle of mass m executes simple harmonic motion under a restoring force with force constant k and amplitude A . If a graph is plotted with the square of its velocity ( v^2 ) on the y-axis and the square of its displacement ( x^2 ) from the mean position on the x-axis, a straight line is obtained. The magnitude of the slope of this straight line is equal to :

Step-by-step solution

For a particle executing simple harmonic motion, the velocity v at a displacement x is given by: v^2 = ^2(A^2 - x^2) where = k m is the angular frequency and A is the amplitude. Rearranging the equation, we get: v^2 = - ^2 x^2 + ^2 A^2 Comparing this with the equation of a straight line y = mx + c , where y = v^2 and x = x^2 , the slope of the line is - ^2 . The magnitude of the slope is ^2 = k m . Answer: k m