Driven SHO Comparison

The driven harmonic oscillator is a standard physics model and the Driven SHO Comparison model displays 51 such oscillators with different natural frequencies driven. The oscillator mass increases from left to right in the multi-oscillator display and the oscillator in the center has a mass of one. All 51 oscillator differential equations are solved simultaneously but the motion or each oscillator is independent of the others because these equations are uncoupled.

where k is the spring constant, b is the damping coefficient, and ω is the frequency of the sinusoidal force. Because the spring constant k and the frequency ω are set equal to one in the model, the natural frequency of oscillation of the center mass coincides with the drive frequency. The time step is chosen to be exactly 1/20 of the drive ω frequency so that 20 clicks of the single-step button advance the model by one drive period.

Questions

Run the simulation and note the red arrow to the left of the oscillators showing the driving force that is applied to each oscillator.

Damped driven harmonic oscillators settle into a steady state after a certain time. How long does it take for the steady state behavior to emerge if b=0.1? If b=0.2?
How does the damping coefficient b affect the maximum displacement of the center mass?
Run the model and describe the steady state pattern at the instant when the driving force is zero? When the force is a maximum? Why are these two patterns different?
Study the analytic solution of the sinusoidally driven simple harmonic oscillator and predict which of the oscillators shown will have a maximum displacement equal to half the maximum displacement of the center oscillator when b=0.1. When b=0.2.