- #1
mahrap
- 37
- 0
So we are given two equations:
$$ \ddot{x} - \dot{x} - x = cost (t) $$
and
$$ x(t) = a sin(t) + b cos(t) $$
The question asks to find a and b.
How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what system of equations would I have to solve? I am completely clueless on how to set up this problem. Any suggestions and hints are appreciated.
$$ \ddot{x} - \dot{x} - x = cost (t) $$
and
$$ x(t) = a sin(t) + b cos(t) $$
The question asks to find a and b.
How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what system of equations would I have to solve? I am completely clueless on how to set up this problem. Any suggestions and hints are appreciated.