For a mass–spring system executing simple harmonic motion, the variation of potential energy with displacement is found experimentally to follow the quadratic relation U=160x2 (U in joules when x is in metres). The total mechanical energy of the system is measured as 0.20 J. Using this information, answer the following:
(i) Obtain the amplitude of oscillation.
(ii) Hence determine the force constant of the spring and the mass of the system if the angular frequency is 8.0 rad s−1.
(iii) Calculate the maximum acceleration experienced by the mass.
(iv) Sketch qualitatively on the same axes the graphs of kinetic energy and potential energy versus displacement, clearly indicating their values at x=0 and at extreme positions.