Logarythmic
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How do I solve
[tex]\ddot{\theta} = c \cos{\theta}[/tex]?
[tex]\ddot{\theta} = c \cos{\theta}[/tex]?
Solve Differential Equation: \ddot{\theta} = c \cos{\theta}
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Numerically. Try Runga Kutta, or for small angles Cos ( [itex]\theta[/itex]) ~ 1 so solve
[tex]\ddot{\theta} = c[/tex]
[tex]\ddot{\theta} = c[/tex]
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Logarythmic said:
Multiply by [itex]2\dot{\theta}[/itex] and then notice that you get
[tex]\frac{d}{dt}\dot{\theta}^{2} = c\frac{d}{dt}{\sin\theta}[/tex]
The rest is easy.
Daniel.
Logarythmic
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Is it? =P
[tex]\dot{\theta}^2 = c_1 \sin{\theta} + c_2[/tex]?
[tex]\dot{\theta}^2 = c_1 \sin{\theta} + c_2[/tex]?
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Yes, now separate variables and integrate.
Daniel.
Daniel.
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"The rest is easy"!
Logarythmic
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Ok, so now I got the integral
[tex]\int \frac{d\theta}{\sqrt{c - \frac{3g}{L}sin{\theta}}}[/tex]
to solve. Any tip?
[tex]\int \frac{d\theta}{\sqrt{c - \frac{3g}{L}sin{\theta}}}[/tex]
to solve. Any tip?
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Yes, use the web integrator from Mathematica's website:http://integrals.wolfram.com/index.jsp
The result is
The result is
