A mass 0.4 kg performs S.H.M. with a frequency 16 Hz. At a certain displacement it has kinetic energy 2 J and potential energy 1.2 J. The amplitude of oscillation is

Step-by-step solution

Total energy of the particle is the sum of kinetic and potential energy: E = K + U = 2 + 1.2 = 3.2 J The angular frequency of the simple harmonic motion is: = 2 f = 2 ( 16 ) = 32 rad/s The total energy in SHM is given by: E = 1 2 m ^2 A^2 Substituting the given values: 3.2 = 1 2 0.4 (32)^2 A^2 3.2 = 0.2 1024 A^2 A^2 = 3.2 204.8 = 1 64 A = 1 8 = 0.125 m Answer: 0.125 m