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m=16 lb

k=10 lb/ft

a=2

t(0)=1 ft

t'(0)=0 ft/sec

Through this I determined the DE

x''(t)+4x'(t)+20x(t)=e

^{-t}

with initial conditions mentioned above.

Using the method of m

^{2}+4m+20=0

I got roots of -2±4i

Therefore, my y

_{c}=e

^{-2t}[c

_{1}sin(4t)+c

_{2}cos(4t)]

Next I attempted to solve further the problem, but I did not understand what to do as the examples I could find throughout the internet and my textbook all are regarding F(t)=cos(t) or similar.

Any help or guidance would be appreciated. Unfortunately the problem is due tomorrow morning so any quick help is more preferred ;)

Thanks ,

Matt!