Serway & Jewett — Oscillatory Motion: Problem 31

An object of mass m moves in simple harmonic motion with amplitude 12.0 cm on a light spring. Its maximum acceleration is 108 cm/s². Regard m as a variable. (a) Find the period T of the object. (b) Find its frequency f. (c) Find the maximum speed \( v_{\text{max}} \) of the object. (d) Find the total energy E of the object–spring system. (e) Find the force constant k of the spring. (f) Describe the pattern of dependence of each of the quantities T, f, \( v_{\text{max}} \), E, and k on m.