29 E CALC SSM Find the mechanical energy of a block-spring system with a spring constant of 1.3 N/ cm and an amplitude of 2.4 cm. 30 E An oscillating block-spring system has a mechanical energy of 1.00 J, an amplitude of 10.0 cm, and a maximum speed of 1.20 m/s. Find (a) the spring constant, (b) the mass of the block, and (c) the frequency of oscillation. 31 E A 5.00 kg object on a horizontal frictionless surface is attached to a spring with k = 1000 N/m. The object is displaced from equilibrium 50.0 cm horizontally and given an initial velocity of 10.0 m/s back toward the equilibrium position. What are (a) the motion's frequency (b) the initial potential energy of the block-spring system, (c) the initial kinetic energy, and (d) the motion's amplitude? 32 E Figure 15.20 shows the kinetic energy K of a simple harmonic oscillator versus its position x. The vertical axis scale is set by Ks = 4.0 J. What is the spring constant? K (J) K, -12 -8 -4 0 4 8 12 x (cm)