# Second order differential equation

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1. Dec 1, 2015

### engnrshyckh

i am given an equation which i have to solve in simulink. the equation is quite veered to me. some one help me in understanding what kind of equation it is so that i can solve it in matlab simulink.
(2+x^2)theta'' + (2xx' +1)theta' + 9.8(xcostheta-sinthetha)-x''=T

2. Dec 1, 2015

### SteamKing

Staff Emeritus
I think this is your ODE:

$(2+x^2) ⋅ θ'' +(2x⋅x'+1) ⋅ θ' + 9.8 ⋅ (x\, cos(θ)-sin(θ)) - x''= T$

Is T a constant?
Are you given any initial conditions for x, x', θ, or θ' ?

3. Dec 2, 2015

### engnrshyckh

T=10 and initial condition are zero

4. Dec 2, 2015

### SteamKing

Staff Emeritus
I take it the latter means that x = x' = θ = θ' = 0.

5. Dec 2, 2015

### engnrshyckh

yes it is written in question that initial condition is zero

6. Dec 2, 2015

### engnrshyckh

(2+x2)⋅θ′′+(2x⋅x′+1)⋅θ′+9.8⋅(xcos(θ)−sin(θ))−x′′=T this equation is look like to be some kind of pendulum. if we use Laplace transformation what would happen to x'' and x'.as they must be represent some angular velocity component.

7. Dec 2, 2015

### SteamKing

Staff Emeritus
Since this ODE has mixed terms which are being differentiated and multiplied together, I'm not sure if you could use a LT that you would be able to obtain a closed-form solution.

Right now, the only solution I see is expressing this ODE as a system of first order ODEs and then using a Runge-Kutta numerical technique.

By the way, do x and θ depend on a third parameter, like time?

8. Dec 2, 2015

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9. Dec 2, 2015

### engnrshyckh

here is the snapshot of original problem i have to plot it on simulink. i am confused what to do with x and x' . integrator block of simulink use Runge-Kutta numerical technique.

10. Dec 2, 2015

### SteamKing

Staff Emeritus
It's not clear why you are confused.

x and x' have initial conditions just like θ and θ'. You use these initial conditions as a starting point for solving numerically the system of first-order ODEs you obtain after making appropriate substitutions for x" and θ".