As Retardation is directly proportional to displacement a α - x ⇒ a = - kx F = - kmx Using work energy theorem Work done = change in the Kinetic energy dW = Fdx = - kmxdx Total work done W = ∫ dW = ∫ Fdx = - ∫ kmxdx W = −km
x2
2
Or we can say loss of the Kinetic energy is proprtional to x2