A mass weighing 3lb stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1 in, and then set in motion with a downward velocity of 2ft/s, and if there is no damping, find the position u of the mass at any time t

Question

loser66 · Answer

I have to apply formula 
$$mU'' +\gamma U' + kU=F(t)$$

amistre64 · Answer

its just a second order differential equation

amistre64 · Answer

let u = e^(rx), u' = re^(rx), u'' = r^2e^(rx)

e^(rx) (mr^2 + gr +k) = 0  is the homogenous form

r = (-g +- sqrt(g^2-4mk))/(2m)

which i believe goes into sin/cos stuff

amistre64 · Answer

we have initial conditions to apply to it to solve for the arbitrary constants