# Solve dynamic system using Euler method

Problem Statement

Consider the following dynamic system, Where, K=4 and m=4.

Find out the value of x(t) at the given value of t=2, with initial condition $$x(0)$$ and $$\dot x(0)$$, using the Euler method for numerical integration.

So far, I solved Euler method for differential equation. How could I solve it for dynamic system?

• Your system seems a bit strange... The first equation just becomes $x'(t) = x'(t)$, and the second $x''(t)=-\frac km x(t)+\frac 1m F$. The dependence on $x'$ is only expressed through $F$. – PierreCarre Apr 17 at 21:27
• What was the system you solved using Euler's method? $$\begin{cases} x'(t) = v(t) \\ v ' (t) = -\frac km x(t)+ \frac 1m F \end{cases}$$ ? – PierreCarre Apr 17 at 21:30
• It looks like the harmonic oscillator with a step input, where we study the movement of a mass $m$ on a spring with elastic constant $k$ and with an external force $F$. – Ertxiem Apr 17 at 23:04
• @PierreCarre Yes I am looking for the solution of the system of differential equations as you rightly mentioned in your second comment. – Encipher Apr 18 at 0:38