- #1

tanky322

- 43

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## Homework Statement

Solve the Mass-Spring-Damper Differential equation

mx''+bx'+kx=exp(-t)cos(t) (Where x'' is d2x/dt2 etc, don't know how to do the dots above )

I understand how to solve this problem, but the thing that confuses me is that the right is in terms of "t" and left is in terms of "x". I understand that x is a function of t such that x''=d2x/dt2, but I am confused about how to solve the equation by recurrence relations. Once I expand out each side by its series solutions and group like terms, how do I compare terms of x to terms of t?

For example, if this works out to be:

(a1+3a3)+(a2+4a2)x+(a3+6a5)x^2+...=1+t+t^2/2!+...

Can I say that a1+3a3=1; a2+4a2=1; and a3+6a5=1/2!?

Thanks!