- #1
checkmatechamp
- 23
- 0
Homework Statement
A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s2.
Homework Equations
The Attempt at a Solution
I solve for k and get 64, and solve for the mass and get 32/64, so my differential equation is 0.5y'' + 2y' + 64y = 0, I solve for r and get c1*e^(-2t)*cos(2t*sqrt(31)) + c2*e^(-2t)*sin(2t*sqrt(31))
My initial position is 0, so y(0) = 0, and my initial velocity is -2, so y'(0) = -2
So substituting, I get
0 = c1*e^0*cos(0) + c2*sin(0)
0 = c1
Now for y',
y' = -c1*e^(-2t)*sin(2t*sqrt(31))*2sqrt(31)) + -2c1*e^(-2t)*cos(2t*sqrt(31)) + c2*e^(-2t)*cos(2t*sqrt(31))*2sqrt(31) - 2*c2*e^(-2t)*sin(2t*sqrt(31))
-2 = -c1*e(0)*0 - 2c1e^(0)*cos(0) + c2*e^(0)*cos(0)*2sqrt(31) - 2*c2*e^(0)*sin(0))
-2 = -2c1 + c2*2sqrt(31)
But c1 is 0, so -2 = c2*2sqrt(31), and so c2 = -1/sqrt(31)
So my final equation is -1*e^(-2t)*sin(2t*sqrt(31))/sqrt(31)
But when I pick that as an option, the computer marks it wrong. I see some options with a 12sqrt(31) on the bottom, but I don't think that's it.