Synopsis

Simple harmonic motion (SHM):  equation of un-damped oscillation for a mass on a spring, its solution, relative phases of displacement, velocity and force.  Effect of a constant force such as gravity.  Energy in SHM.  Use of equation of motion and/or energy method to study examples of SHM and approximate SHM, including simple pendulum and diatomic molecule.

Phasor diagrams: superposition of oscillations, interference, beats.

SHM using complex numbers: use of complex numbers to denote amplitude and phase of SHM. 

Damped oscillations: light, heavy and critical damping; amplitude and energy decay; quality factor.

Forced oscillations: frequency response and resonance.  

Revision of electrical circuits:  voltage, current and charge in circuits; electrical resistance; resistors in series and parallel; Kirchhoff's laws.  Inductors and capacitors.  Circuits with exponential decays: discharge of a capacitor through a resistor, decay of current through an inductor.

Oscillations in electrical circuits and complex impedance:  Oscillation in an LC circuit, relative phases of voltages, charge and current.  Damped undriven oscillations in an LCR circuit.  Complex current and voltage. Complex impedance and its application in resistors, capacitors, inductors and simple circuits. Electrical resonance in an LCR circuit, simple filter, bandwidth, Q factor. Mechanical impedance. Relationship of behaviours seen in electrical systems to those of mechanical systems.