Problem Statement

Consider the following dynamic system, Dynamic System Where, enter image description here

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?

  • $\begingroup$ 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 $F$. $\endgroup$ – PierreCarre Apr 17 at 21:27
  • $\begingroup$ What was the system you solved using Euler's method? $$ \begin{cases} x'(t) = v(t) \\ v ' (t) = -\frac km x(t)+ \frac 1m F \end{cases} $$ ? $\endgroup$ – PierreCarre Apr 17 at 21:30
  • $\begingroup$ 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 $F$. $\endgroup$ – Ertxiem Apr 17 at 23:04
  • $\begingroup$ @PierreCarre Yes I am looking for the solution of the system of differential equations as you rightly mentioned in your second comment. $\endgroup$ – Encipher Apr 18 at 0:38

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