Solve Differential Equation: \ddot{\theta} = c \cos{\theta}

[Logarythmic]

How do I solve

$$\ddot{\theta} = c \cos{\theta}$$?

 

[Integral]

Numerically. Try Runga Kutta, or for small angles Cos ( $\theta$) ~ 1 so solve

$$\ddot{\theta} = c$$

 

[dextercioby]

How do I solve

$$\ddot{\theta} = c \cos{\theta}$$?

Multiply by $2\dot{\theta}$ and then notice that you get

$$\frac{d}{dt}\dot{\theta}^{2} = c\frac{d}{dt}{\sin\theta}$$

The rest is easy.

Daniel.

 

[Logarythmic]

Is it? =P

$$\dot{\theta}^2 = c_1 \sin{\theta} + c_2$$?

 

[dextercioby]

Yes, now separate variables and integrate.

Daniel.

 

[HallsofIvy]

"The rest is easy"!

 

[Logarythmic]

Ok, so now I got the integral

$$\int \frac{d\theta}{\sqrt{c - \frac{3g}{L}sin{\theta}}}$$

to solve. Any tip?

 

[dextercioby]

Yes, use the web integrator from Mathematica's website:http://integrals.wolfram.com/index.jsp

The result is