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## Homework Statement

a) ẍ + 5ẋ + 4x = 0

x(0) = 0, ẋ(0)=1

What type of damping?

b) ẍ + x = cos(t)

x(0) = 0, ẋ(0)= 1

What type of motion?

## The Attempt at a Solution

a) Let x = R Eᴿᵀ

R = -4

R = -1

x(t) = CE**-4T + DE**-t

C + D = 0

-4C - D = 1

C = 1/5

D = 1/5

And it is over damping

I think this is the right answer for a) but i have no idea how to do b)