Question

We consider a spring mass system. We use standard international system of units, the mass is 1kg and the change of magnitude of force |∆Fs| (in unit of Newton, 1N = 1kg ∗ m/s2) from the spring is 9 times the change of length of the spring |∆x|(in meter), i.e |∆Fs| = |9∆x|, the spring is a linear spring with spring constant equal to 3 in Hook’s law. The equilibrium position is at x = 0. When the external forcing has frequency same as the natural frequency, the type of motion, possessing an oscillation with growing amplitude, which is called resonance.

(a) Write down the initial value problem (differential equation and initial values) if external force is cos3t, and initially the mass is at rest.

(b) Solve the above initial value problem.

(c) Finally draw the solution in (t,y)-plane. What is the natural frequency of the spring mass system.

Answer 1