Question

Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 3kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 3 N.s/m, and the forcing function is F(t) = 9sin (3t).

Answer 1

3x''+3x'+7x = 9sin 3t - to begin
then Use the method of undetermined coefficients
`xp=Asin(3t)+Bcos(3t).`
Then you need to find x′p and x′′p and sub them into equation, that will help you to solve A and B.

`xp=Asin(3t)+Bcos(3t) x'p=3Acos(3t)−3Bsin(3t) x''p=−9Asin(3t)−9Bcos(3t)`
And finally you will have this :
3x′′+3x′+7x=9sin(3t)[−27Asin(3t)−27Bcos(3t)]+[9Acos(3t)−9Bsin(3t)]+[7Asin(3t)+7Bcos(3t)]=9sin(3t)(−20A+9B)sin(3t)+(−20B+9A)cos(3t)=9sin(3t)