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jrsweet
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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??