How to solve a simple symbolic identity?

I have the following identity.

The solution is .

I wrote the following code.

syms w0 a b t m F0;
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
sol = solve(eqn, [a b])

sol = struct with fields:
    a: -(F0*cos(t*w0))/(2*m*w0*sin(t*w0))
    b: 0

The sol is not what I want to get.

Could you tell me how to get the correct a and b, i.e., ?

Answer 1

[DH]

Thank you VBBV.

Based on your reply, I wrote the following code:

syms w0 a b t m F0;
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
eq1 = subs(eqn, t, 0.5);
eq2 = subs(eqn, t, 0.6);
sys_eqn = [eq1 eq2];
sol = solve(sys_eqn, [a b])

sol = struct with fields:
    a: 0
    b: F0/(2*m*w0)

Answer 2

[VBBV]

syms w0 a b t m F0
eqn = 2*b*w0*cos(w0*t) - 2*a*w0*sin(w0*t) == (F0*cos(w0*t))/m;
sol = solve(eqn, [b])

sol = 

b = subs(sol,t,0)

b = 

[VBBV]

Solve for b variable and substitute t as zero, since you have only one equation, you can solve for only one variable. The solution to a doesnt exist for t = 0.