Modeling a Damped Oscillator in a Viscous Fluid

[yournamehere]

Homework Statement

A mass m of 5 kg stretches a spring about 0.1m. This system is placed in a viscous fluid.
Due to the fluid a braking force of 2N acts on the mass if the velocity is 0.04m/s. For the acceleration of gravity we can assume g = 10m/s^2.

Set up from the balance of forces for spring force FF (t) = −Du(t), damping FD(t) = −(miu)u′(t) and inertia FT (t) = −mu′′(t) the appropriate differential equation and find the general (real) solution.

The mass is released 1m from its position of rest. Compute the solution of this initial value
problem.

Homework Equations

The Attempt at a Solution

FF(t) + FD(t) + FT(t) + Braking Force FB + Gravitational Force FG = 0?

 

[gabbagabbahey]

In this case, the breaking force is FD (and you can determine "miu" from the information you are given), so what is your ODE?

 

[yournamehere]

soooooo...

i think i got it..

D=m*g/s=5*10/0.1=500


sigma=F/v = 2N/0.04m/s=50

right?