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:
a. (i) Obtain the amplitude of oscillation.
b. (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.
c. (iii) Calculate the maximum acceleration experienced by the mass.
d. (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.