Seventeen balls are coupled by springs in such a way that the restoring force is proportional to the difference in height between two neighboring balls. The left hand ball is driven and the right hand ball is impedance matched. The mass of the small balls is one and the mass of the larger balls near the center is 4.0. The spring constant connecting the balls is one. The length of the entire chain is 2*pi.
Set the desired frequency and run the simulation until the steady state is reached.
What functional form describes the amplitude of the heavy balls when the angular frequency is 1.02? 1.1?
What functional form describes the amplitude of the heavy balls when the angular frequency is 0.8?
Can the amplitude of oscillation of the heavy balls ever be larger than the amplitude oscillations of the balls to the left of the barrier? To the right of the barrier?
How is the motion of the smaller balls on the left and right side of the barrier different?