Let the ends of the spring (see Problem 3.4.12) move with different frequency:
x₁ = A₁cosω1t, x₂ = A₂cosω2t. How does the force of spring tension change with
time in this case? Construct a graph of the time dependence of the force of
tension in the case of close frequencies. Why can we talk about beating here?
Determine in the case of unequal amplitudes and frequencies the average energy of the spring over a large time.