Find coefficients after rearranging harmonic terms

I am trying to find the coefficients of sin(w*t), cos (w*t), sin(2*w*t) and cos(2*w*t) in the expression 'f'

Here is the code

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clc

syms A11 A12 A21 A22 B1 B2
syms A0 B0 A1 B1 C1 D1
syms w t
syms Ps Pc
syms km 

th=A0*cos(w*t)+B0*sin(w*t)+B1*cos(2*w*t)+B1+C1*sin(2*w*t);
thd=diff(th,t);
thdd=diff(th,t,2);

f=thdd-(A21-A22*(1+km*(sin(w*t)*Pc+cos(w*t)*Ps)))*thd-(A22*w*km*(cos(w*t)*Pc-sin(w*t)*Ps))*thd+B1*w*cos(w*t);

But I am finding it difficult to rearrage the expression, interms of sin(w*t), cos (w*t), sin(2*w*t) and cos(2*w*t)

[C,T] = coeffs(f,{sin(w*t),cos(w*t),cos(2*w*t),sin(2*w*t)})

Any help.

Thank You

Answer 1

[Star Strider]

Try this:

syms A11 A12 A21 A22 B1 B2 A0 B0 A1 B1 C1 D1 w t Ps Pc km 
th(t) = A0*cos(w*t)+B0*sin(w*t)+B1*cos(2*w*t)+B1+C1*sin(2*w*t);
thd=diff(th,t);
thdd=diff(th,t,2);
f=thdd-(A21-A22*(1+km*(sin(w*t)*Pc+cos(w*t)*Ps)))*thd-(A22*w*km*(cos(w*t)*Pc-sin(w*t)*Ps))*thd+B1*w*cos(w*t);
fc = collect(f, [sin(w*t) sin(2*t*w) cos(w*t) cos(2*t*w)])                      % Collected Terms
[fcc,T] = coeffs(f, [sin(w*t) sin(2*t*w) cos(w*t) cos(2*t*w)])                  % Coefficients & Terms

produces:

fc(t) =
(- A0*A22*Ps*km*w^2 - A0*A22*Pc*km*w)*sin(t*w)^2 + (- 2*A22*B1*Ps*km*w^2 - 2*A22*B1*Pc*km*w)*sin(t*w)*sin(2*t*w) + (A22*B0*Pc*km*w - A0*A22*Ps*km*w + A0*A22*Pc*km*w^2 + A22*B0*Ps*km*w^2)*sin(t*w)*cos(t*w) + (2*A22*C1*Ps*km*w^2 + 2*A22*C1*Pc*km*w)*sin(t*w)*cos(2*t*w) + (- B0*w^2 + A0*(A21 - A22)*w)*sin(t*w) + (2*A22*B1*Pc*km*w^2 - 2*A22*B1*Ps*km*w)*sin(2*t*w)*cos(t*w) + (- 4*C1*w^2 + 2*B1*(A21 - A22)*w)*sin(2*t*w) + (- A22*B0*Pc*km*w^2 + A22*B0*Ps*km*w)*cos(t*w)^2 + (- 2*A22*C1*Pc*km*w^2 + 2*A22*C1*Ps*km*w)*cos(t*w)*cos(2*t*w) + (B1*w - A0*w^2 - B0*w*(A21 - A22))*cos(t*w) + (- 4*B1*w^2 - 2*C1*(A21 - A22)*w)*cos(2*t*w)
 
fcc(t) =
[ - A0*A22*Ps*km*w^2 - A0*A22*Pc*km*w, - 2*A22*B1*Ps*km*w^2 - 2*A22*B1*Pc*km*w, A22*B0*Pc*km*w - A0*A22*Ps*km*w + A0*A22*Pc*km*w^2 + A22*B0*Ps*km*w^2, 2*A22*C1*Ps*km*w^2 + 2*A22*C1*Pc*km*w, - B0*w^2 + A0*(A21 - A22)*w, 2*A22*B1*Pc*km*w^2 - 2*A22*B1*Ps*km*w, - 4*C1*w^2 + 2*B1*(A21 - A22)*w, - A22*B0*Pc*km*w^2 + A22*B0*Ps*km*w, - 2*A22*C1*Pc*km*w^2 + 2*A22*C1*Ps*km*w, B1*w - A0*w^2 - B0*w*(A21 - A22), - 4*B1*w^2 - 2*C1*(A21 - A22)*w]
 
T(t) =
[ sin(t*w)^2, sin(t*w)*sin(2*t*w), cos(t*w)*sin(t*w), cos(2*t*w)*sin(t*w), sin(t*w), cos(t*w)*sin(2*t*w), sin(2*t*w), cos(t*w)^2, cos(t*w)*cos(2*t*w), cos(t*w), cos(2*t*w)]