The data given was the acceleration of the component over time, as below:
time | Acceleration (m/s²)
0 | 0
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.
- I was required to construct the 3rd degree equation
- Generate the differential equation
- Determine the oscilation
- Solve the equation knowing that y(0)=0 and y'(0)=0 (So i get Constant1 and Constant2)
- 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
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.