a. Two balls of mass m, which are connected to each other and to the walls by three springs of stiffness k, are simultaneously given the same modulo velocity directed along the springs. Find the frequency of oscillation of the balls if their velocities are oppositely directed / equally directed.
b. Free vibrations of complex systems are the sum (superposition) of several harmonic oscillations with different frequencies. If the first ball in Problem 3.4.15a is given a velocity v along the spring, then the subsequent motion of the balls will be the sum of two motions: the motion of the balls given a velocity v/2 and −v/2, and the motion of the balls given a velocity v/2 and v/2. Use this to determine the velocity of the balls at the moments following the beginning of the oscillations. What is the maximum displacement of the first ball? the second ball? the maximum elongation of the middle spring?
c. Solve the problem 3.4.15b if the first ball has a velocity 3v and the second one has a velocity v.