I am a joiner mechanical engineer student, and I really need help with studying and understanding Vibration and Machine design. I do like both subject and really want to understand them but I am not a 100% clear un them yet, and the book I am using is weak on clarifying and showing some of the concepts. I am using shigley's for Machine design and Schaum's for vibration. If any book out there that you recommend, some video lecture, or even example problems that would greatly help. I will also list some of the area's that I need help with.

Vibration:
* Help me better on how to set my equation of a motion
* Finding my natural frequency,
* Impulse response, with and without additional harmonic forcing
* 1DOF Convolution integral
* Obtaining 2DOF EOM and putting in matrix form
* Free response for 2DOF undamped system (wn, mode shapes, and x(t))
* Free response for 2DOF damped systems (wn only)
* Forced response for both undamped and damped 2DOF systems

Machine Design:
* Determining stress in an object under combined loading
* Beam deflection using Castigliano's Theorem
* Beam buckling
* Static failure analysis

Thank you so much for the help, I really need it.