As indicated by the cart-with-flywheel example discussed in this section, an unbalanced ro...

As indicated by the cart-with-flywheel example discussed in this section, an unbalanced rotating machine part typically results in a force having amplitude proportional to the square of the frequency ω. (a) Show that the amplitude of the steady periodic solution of the differential equation

Thus the resonance frequency in this case is larger (in contrast with the result of Problem) than the natural frequency ω0 = √k/m. (Suggestion: Maximize the square of C.)