In a spring-block system executing SHM, at displacement

Solution

In a spring-block system undergoing simple harmonic motion (SHM) , the total mechanical energy E is constant and given by: E = KE + PE = (1/2) kA² At any displacement x, the potential energy is: PE = kx²/2 And the kinetic energy is the remaining part: KE = (k/2)(A² - x²) At x = A/2, PE = k(A/2)²/2 = kA²/8 KE = (k/2){A² - (A/2)²} KE = (k/2)(A² - A²/4) KE = 3kA²/8 We are asked to find the ratio KE/PE at x = A/2 The ratio of kinetic to potential energy at displacement x=A/2 is 3:1.