Physics · University
Driven oscillations, damping and resonance · revision notes
A linear mass-spring oscillator obeys mx″+kx=0. Its natural angular frequency is sqrt(k/m), not k/m.
Key ideas and conditions
Free motion
A linear mass-spring oscillator obeys mx″+kx=0. Its natural angular frequency is sqrt(k/m), not k/m.
Damping
A viscous damping force −bx′ converts the equation to mx″+bx′+kx=0. In underdamping, the oscillation envelope decays exponentially.
Driving
A periodic external force can transfer energy to the oscillator. The steady response depends on drive frequency, damping and phase.
Resonance
A finite drive does not imply infinite amplitude in a damped physical oscillator. Transient motion and nonlinear limits matter.
Explain without looking
- A displacement is x=A cos(ωt). What is its acceleration?
- Describe an experiment using a recorded decay envelope to estimate damping, without prescribing a hazardous apparatus.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.