Activities

1. With the default settings you can see that with the harmonic oscillator (γ = f = 0) the elongation phasor rotates with the constant angular velocity ω.
2. Check Graph to see the familiar x(t) curve, which repeats with period 2π/ω.
3. Enable Velocity to see the velocity phasor and its evolution. Which is the angle between both phasors?
4. Enable Acceleration to see the corresponding phasor. Which is the angle between elongation and acceleration phasors?

• How would change your answers to the previous questions with damping (say γ = 0.1)? Check your guess by means of the simulation.
• What happens with f > 0? You should be able to see two very different behaviors: the initial transitory and the final steady state solution.
• With Ω ≅ ω, you should get resonance.
• With f > 0, set γ = 0 and N = 2000. What kind of solution will you expect when Ω/ω is a simple fraction (1/2, 3/2, and so on) and with values like Ω/ω = 1.1274265? What would happen with a truly irrational quotient?