How do you solve a differential equation for mechanical vibrations homework?

[jrsweet]

Homework Statement

A mass m=4 is attached to both a spring, with spring constant k=37, and a dash-pot with damping constant c=4.

The ball is started in motion with initial position x0=1 and initial velocity v0=8 .
Determine the position function x(t).

Homework Equations

The Attempt at a Solution

So, the differential equation would be:
4x''+4x'+37x=0
4r^2+4r+37=0
r=-(1/2)+or- (1/2)sqrt(26)i

And so,
x(t)=e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))
x'(t)=-.5e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))+e^(-.5t)(-.5*C1sqrt(26)sin(.5sqrt(26)t)+.5*C2sqrt(26)cos(.5sqrt(26)t))

x(0)=C1=1
x'(0)=.5sqrt(26)C2-.5C1=8
=.5sqrt(26)C2=17/2
C2=17/sqrt(26)

And so,
x(t)=e^(-.5t)(cos(.5sqrt(26)t)+(17/sqrt(26))sin(.5sqrt(26)t))


Can anyone see anything wrong with this??

 

[tiny-tim]

Hi jrsweet!

(have a square-root-: √ and try using the X² tag just above the Reply box )

Where did your √26 come from?