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MODULE $12($CLO $2,3,4-20$pts$)$

The motion of a damped spring$-$mass system is described by the following ODE:

$m\frac{d^{2}x}{d{t}^2}+c\frac{dx}{dt}+kx=0$

where: $x-$displacement from the initial position in meters, t $-$ time in seconds, $m=20kg,c-$ damping coefficient $=40N-\frac{s}{m},$ Spring constant, $k=20\frac{N}{m}.$ Initial velocity is zero and initial displacement is $1$ m $.$ Determine the displacement after $5$ seconds, use $h=1sec.$ Note: $d\frac{x}{d}t-$ velocity and $d^{2}xd{t}^2-$ acceleration.

Use Euler's Method to solve second order ODE. $($No need for second guess since the initial value of dxdt is given already$)$

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