Consider a simple harmonic motion (SHM). Let K and U be kinetic energy and potential energy when the displacement in SHM is one-half ( 1 2 ) the amplitude. Which of the correct statement?

Step-by-step solution

Potential energy of a body performing SHM is given by U= 1 2 k x^2 Here, x is the displacement of the body from mean position. Given, x= a 2 [ a= amplitude ] U= 1 2 k ( a 2 )^2 U= 1 2 k a^2 4 ( i ) Now, kinetic energy of this body is given by K= 1 2 m v^2= 1 2 m ^2 (a^2-x^2 ) K= 1 2 K (a^2-x^2 ) Given, x= a 2 K= 1 2 K (a^2- a^2 4 ) K= 1 2 k 3 a^2 4 ( ii ) From Eqs. (i) and (ii), we get K U = 1 2 k 3 a^2 4 1 2 k a^2 4 = 3 1