Dynamics cheat sheet

Where
F n = 2 T
F 0 = 2 T
∫ T
0
∫ T
0
2π
−in
f (t) e T t dt
f (t) dt
Another way to write the above is to use the classical representation using cos and sin. The same coefficients
(i.e. the same series) will result.
˜f (t) = a 0 +
a 0 = 1 T
n=1
∫ T
0
a n = 1
T/2
b n = 1
T/2
N∑
a n cos n 2π N T t + ∑
b n sin n 2π
T t
f (t) dt
∫ T
0
∫ T
0
n=1
(
f (t) cos n 2π )
T t dt
(
f (t) sin n 2π )
T t dt
Just watch out in the above, that we divide by the full period when finding a 0 and divide by half the period
for all the other coefficients. In the end, when we find ˜f (t) we can convert that to complex form. The complex
form seems easier to use.
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