Driven Oscillator

Questions

A simple harmonic oscillator is driven by an external force in addition to the internal restoring force and friction.

• Find the spring constant. (Hint:  Apply a constant force.)
• Find the mass.
• Drive the frequency at resonance and explain the behavior of the position graph.  How the the behavior change with and without friction.
• Puzzle. Drive the system with a function that switches a constant force on and off.  This can be achieved with the step function:  step(sin(t/4)).  The step function is zero if the argument is negative and one if the argument is positive.  The given function, step(sin(t/4)), will therefore produce a square wave with amplitude of one and an angular frequency of one quarter.  Why does the system oscillate, stop, and oscillate again?  Does this behavior occur at any other frequencies.  For example, notice that the function step(sin(t/4.5)) produces qualitatively different behavior.  Why is this?