# Assignment 1#

We consider here a mass-damper-spring system as shown in the figure below.

Exercise a)

Write the system equation as a second order differential equation. The spring is relaxed when the wagon is at the position \(x=0\).

Hint

Have you watched lecture 2?

Exercise b)

Transform the second order equation into a set of two first order equations.

Exercise c)

Write a code for simulating the system equations from b), using the Euler forward integration method a step size of \(0.01\) seconds. The mass \(m\) is 1kg, the linear spring coefficient \(k\) is 1 N/m, and the linear damping coefficient is 0.7 Ns/m. To get going, you will also need values for the initial states (i.e. the states at the time step \(j=0\)). Set the initial position to be 1 meter away from the equilibrium position of the spring (either side is OK), and the initial velocity to be 0.