Problem Sets and Exams will induce less panic if you clue in on key phrases and concepts.
Make sure you are familiar with the following:
Time Constants
(tau) for 1st order system of this form: "K / (Ts + 1)", tau=T.
Steady State (or "final") value of 1st order system above is simply 'K' (set s=0; i.e. dt=0)
Time to reach "99%" of final value for 1st order system with time constant "T" (tau) ? Straight-forward:
Since system has exponential decay, time needed = n*T, where 'n' can found by taking natural log:
log(.01) = -4.6, so 4.6 tau ('T') are required.
log(.02) = -3.9, so 3.9 tau gets you to (1-.02) = 98% of final value
log(.05) = -3.0, so 3.0 tau gets you to 95%
State Equation formulation for describing a system
dx/dt = Ax + Bu ...... [x = vector of state variables]
dy/dt = Cx + (Du) ...... [y = output of interest to you, D has been 0 for us in 2.010]
Transfer Function ("TF") representation (Output/Input)
Bode Plot (aka Frequency Response)
Step Response (aka Transient Response)
Eigenvalues (lambdas = roots of the polynomials in the NUM and DEN of the transfer function)
Mode Shapes "exp(lambda*t)" type solutions using eigenvalues can form (some combination of):
- Harmonic responses (oscillations; waves),
- Exponential decay,
- Exponential growth, or a
- Steady value (exp(0)).
Also Note that MATLAB can often do a lot of the legwork for you!
...Just make sure a problem does not explicitly ask you to plot or derive things yourself.