Mostly single degree of freedom systems will be considered. System modelling and linearisation using free body diagrams and energy methods. The solution to the free vibration of undamped and damped systems. Forced response to harmonic, rotating unbalance and base excitations. The response to generalised forcing functions. Steady state vibration analysis, vibration isolation methods and alternative models for damping. Vibration measurement techniques, the base excitation problem. Multiple degree of freedom systems will be introduced. The matrix notation, state vector formulation and the modelling of lumped parameter systems will be shown leading to the eigenvalue problem and modal analysis.