# Differential equation for a vibration problem

## Homework Statement

The data given was the acceleration of the component over time, as below:
time | Acceleration (m/s²)
0 | 0
0,2 |3,61
0,4 |4,5
0,6 |5,4
0,8 |7,508
1 |12

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The Rigidity constat is 12600000 [N/m] (for the spring)
The damping constant is 6500 [N/m] (for the damp)

The system has 2 of each.

## Homework Equations

1. I was required to construct the 3rd degree equation
2. Generate the differential equation
3. Determine the oscilation
4. Solve the equation knowing that y(0)=0 and y'(0)=0 (So i get Constant1 and Constant2)
5. Generate graphics for y(t) from 0 < t < 3s

## The Attempt at a Solution

For nº 1 i got the following:
f(t) = 3600 * (33,697*x^3 - 46,4018*x^2 + 24,693*x + 0,0615)

For nº 2:
Knoginw that, C=6500 * 2 = 13000 and K=12600000 *2 = 25200000

So,
3600*y''+13000*y'+25200000*y= 121309,2*x^3- 167043,6*x^2 + 88834,3*x + 221,4

for the particular solution i used:
A*x^3 + B*x^2 + C*x + D

got the info of A,B,C and D and replaced.

Got the following:
y(t) = e^-1,8*t * [C1*cos(83,647*t)+C2*sen(83,647*t)]+ 4,81*(10^-3) * t^3 - 6,64*(10^-3) * t^2 + 3,523*(10^-3) * t +1,57*10^-5

And the problem goes on...

What i need \/
The point is, I'd like to port all this info to Matlab or Geogebra or whatever software you recommend, but i have no idea on how to, would be anyone able to help ?

I'd like to get the A,B,C and D, plus C1 and C2 and them generate the graphs, all on the software, using the data given.