A particle executes a simple harmonic motion of amplitude A . The distance from the mean position at which its kinetic energy is equal to its potential energy is

Step-by-step solution

The kinetic energy K and potential energy U of a particle executing simple harmonic motion with amplitude A at a distance x from the mean position are given by K = 1 2 k(A^2 - x^2) and U = 1 2 k x^2 , where k is the force constant. Given that the kinetic energy is equal to the potential energy, we set K = U : 1 2 k(A^2 - x^2) = 1 2 k x^2 Simplifying the equation: A^2 - x^2 = x^2 A^2 = 2x^2 x^2 = A^2 2 x = A 2 Using the value 2 1.414 , we calculate: x = A 1.414 0.707 A Rounding to two decimal places, we get x = 0.71