There is a body having mass m and performing SHM with amplitude ' a '. There is a restoring force F=-Kx , where x is the displacement. The total energy of the body depends upon which of the following?

Step-by-step solution

The restoring force is given by F = -Kx . The potential energy of the body at displacement x is U = 1 2 Kx^2 . The kinetic energy of the body is K.E. = 1 2 mv^2 = 1 2 m ^2(a^2 - x^2) . Since ^2 = K m , the kinetic energy can be written as K.E. = 1 2 K(a^2 - x^2) . The total energy of the body is E = U + K.E. = 1 2 Kx^2 + 1 2 K(a^2 - x^2) = 1 2 Ka^2 . Thus, the total energy depends only on the force constant K and the amplitude a . Answer: K, a