Explain how resonance occurs for a driven oscillating system and describe the effect of damping on the resonant frequency.

When the driving force occurs at the natural frequency of the system (the natural frequency being the frequency if the system were oscillating freely) there is maximum energy transfer to the system causing the amplitude of oscillations to increase.
When damped, the peak of the amplitude vs driving frequency graph shifts down and slightly to the left (would show on graph). Thus the resonant frequency decreases slightly.