Oscillations

You will be able to

• Define simple harmonic motion by a = −ω²x and use x = x₀ sin ωt and v = ±ω√(x₀² − x²).
• Use ω = √(k/m) and ω = √(g/l) to determine the period of a mass–spring system and of a simple pendulum.
• Describe the interchange between kinetic and potential energy and calculate the total energy ½mω²x₀².

You will be able to

• Describe light, critical and heavy damping and sketch displacement–time graphs for each.
• Explain resonance: maximum amplitude when the driving frequency equals the natural frequency f₀ = (1/2π)√(k/m).
• Describe how heavier damping lowers and broadens the resonance peak and shifts it slightly below f₀.