Ok I find the function to be \theta (t) = \frac{\theta_0}{2} (exp (i \sqrt\frac{g}{L} t) + (exp (-i \sqrt\frac{g}{L} t)
Now to find the period of oscillation I need to find the times between where \theta (t) = 0 , which only occurs at t=0...
Any help on how to find these periods? Thx.
Thank you for the reply, it was helpful. I am still have much difficulty with this problem though. I have never taken diff. eq. class, the teacher wants us to 'discover' these solutions :rolleyes:
I don't think X^{\prime\prime}(x)+\frac{k^2}{\alpha^2}=0 is what I want to solve is it? I want...
I stand corrected.
I don't think the buoyant force would act on that bug would it?
If a body displaces fluid then I don't think surface tension would have much of an effect, for example in a boat.
Homework Statement
The temp. as a function of time of a metal rod obeys the following diff. eq.
\alpha^2 \frac{\partial^2u(x,t)}{\partial x^2} = \frac{\partial u(x,t)}{\partial t}
Use separation of variables to find u(x,t) in a rod of length 1 subject to the conditions u(0,t) = 0 ...
Ok, I have used the Euler method and found the period to be roughly 2 second.
Now I need to make the small angle approximation, and compare the results.
I make the approximation and solve the differential equation to get \theta(t) = \alpha e^{i\sqrt{\frac{g}{L}}t}+\beta...
No, I can't do that... Thats the second part of the problem. Then for the third part I have to state where the small angle approximation breaks down (using the first two parts).
So, here is where I am at... I need to solve this thing numerically somehow. I messed with Maple a bit and...
Hello,
I have never taken a differential equations class. I have this problem that I could really use some help on.
Thx
Homework Statement
A pendulum' motion is the following equation \ddot\theta = (\frac{-g}{l})\sin(\theta))
I need to find the period of oscillations for various starting...