Question

Differential Equations: A spring is stretched 4 inches by a mass that weighs 8 pounds. The mass is attached to a dashpot mechanism that has a damping constant of (1/4) lb-sec/ft and is acted upon by an external force of 5sin(2t) pounds. The differential equation that governs the displacement u(t) of the mass is: ?

I started by getting the spring constant, which is mg/L. I set mg = 8 and L = 4, so the spring constant k = 2. So I have an equation like this:

8u'' + (1/4)u' + 2u = 5sin(2t)
The answer is u'' + u' + 96u = 20sin(2t). What have I done wrong?

Answer 1

how did you get the k=2?

Answer 2

Figured it out... you need to divide the weight (8) by the gravity (32), which gives you m = (1/4).

Then, to find k, you take the weight and divide it by the length in feet. So it's 4 inches = (1/3) feet. 8/(1/3) = 24 = k. So this is the equation:

(1/4)u'' + (1/4)u' + 24u = 5sin(2t)

simplify it out and you get: u'' + u' + 96u = 20sin(2t)

Answer 3

ok good thats more like it