Damped harmonic oscillator of spring

[katiandss]

Homework Statement

A spring is elastically stretched 10 cm if a force of 3 Newtons is imposed. A 2 kg mass is hung from the spring and is also attached to a viscous damper that exerts a restraining force of 3 Newtons when the velocity of the mass is 5 m/sec. An external force time function f(t) (defined as positive upward) is applied to the mass.

Write down a differential equation model for u(t), the upward displacement of the mass from its equilibrium position at time t.

Homework Equations

Since we are asked for the the differential equation model we are not given any equations.

The Attempt at a Solution

I've solved for the spring constant k within the first sentence-it is 30 kg/s^2. Since this is actually a math class I'm in...my physics is a little rusty and I need help setting up the model to be able to perform the subsequent operations on it. Help would be appreciated and I would greatly appreciate any explanations as to why it is that equation.

 

[vela]

You need to apply Newton's second law$$\sum F = ma$$