1. Explain the concept of modes of vibration, and the difference between single-, two- and multi-degree-of-freedom vibrating systems.[a4]
2. Formulate the equation of motion of an undamped, single degree-of-freedom vibration system using both energy methods and Newton's laws of motion. [a4]
3. Explain the difference between free and forced vibration. [a1]
4. Formulate the equations of motion of vibrating systems with viscous damping and hysteretic damping. [a4]
5. Explain the effect of damping on vibration response both in the time domain and in the frequency domain. [a4]
6. Derive the equations of motion of lumped parameter, multi-degree-of-freedom systems using matrix methods. [a2],[a4],[k4]
7. Apply Lagrange's equation to derive equations of motion of simple vibrating systems, with single or multi-degree of freedom. [e],[k4]
8. Obtain estimates for the lowest natural frequencies of continuous systems using Rayleigh's principle. [a2]
9. Understand Hamilton's principle, and its applications to vibrating systems.[a1],[a2]
10. Analyze SDOF nonlinear systems and obtains graphical solutions in the phase space based on Duffing's equations or van der Pol's equations.[a1],[a3]
Note: The letters within the brackets indicate the general program outcomes of mechanical engineering. See: ME Program Outcomes.