Gain and Phase Shift

Part 4: Resonant Frequency

You saw in Parts 2 and 3 that the gain function M has a unique maximum value. That is, there is an input frequency omega that maximizes gain. This frequency is called the resonant frequency of the system.

1. Use your helper application to find a formula for the value of omega (in terms of c and k) that maximizes M(omega).
2. Find a formula for the maximum gain in terms of c and k.
3. Reality check: The right formulas for resonant frequency and maximum gain should be consistent with your calculations in previous parts of this module. Demonstrate that this is so -- or resolve the inconsistency.