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Gothican
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The total energy of a pendulum is calculated either by it's maximum height (Gravitational Potential), or by the lowest point with maximum velocity (Kinetic Energy).
For the significant formulas of a pendulum see http://en.wikipedia.org/wiki/Pendulum_(mathematics)" wiki page
If you use the highest point to figure out the total energy you'll probably use E = M*g*h - right?
then h = A*sin([tex]\theta[/tex]0) where A is the Amplitude, and [tex]\theta[/tex]0 is the angle of swing. & A = L*sin([tex]\theta[/tex]0) with small angles, and L is length of the rod.
So E = M*g*L*[tex]\theta[/tex]0^2 (sin([tex]\theta[/tex]0) = [tex]\theta[/tex]0)
But if we use the maximum kinetic energy to figure out the total energy, then it would be E = [tex]\frac{M*v^2}{2}[/tex].
Now if v = A*[tex]\sqrt{\frac{g}{L}}[/tex] where L is length of the rod.
Then E = [tex]\frac{M*A^2*g}{2*L}[/tex]
A = L*sin([tex]\theta[/tex]0) with small angles
E = (M*g*L*[tex]\theta[/tex]0^2)/2 (sin([tex]\theta[/tex]0) = [tex]\theta[/tex]0)
Whoever my have noticed, the last calculation is half the energy of the first.
I haven't managed to find any wrong assumption or miss-calculation.
Did anybody else catch one?
Thanks in advance - Gothican
For the significant formulas of a pendulum see http://en.wikipedia.org/wiki/Pendulum_(mathematics)" wiki page
If you use the highest point to figure out the total energy you'll probably use E = M*g*h - right?
then h = A*sin([tex]\theta[/tex]0) where A is the Amplitude, and [tex]\theta[/tex]0 is the angle of swing. & A = L*sin([tex]\theta[/tex]0) with small angles, and L is length of the rod.
So E = M*g*L*[tex]\theta[/tex]0^2 (sin([tex]\theta[/tex]0) = [tex]\theta[/tex]0)
But if we use the maximum kinetic energy to figure out the total energy, then it would be E = [tex]\frac{M*v^2}{2}[/tex].
Now if v = A*[tex]\sqrt{\frac{g}{L}}[/tex] where L is length of the rod.
Then E = [tex]\frac{M*A^2*g}{2*L}[/tex]
A = L*sin([tex]\theta[/tex]0) with small angles
E = (M*g*L*[tex]\theta[/tex]0^2)/2 (sin([tex]\theta[/tex]0) = [tex]\theta[/tex]0)
Whoever my have noticed, the last calculation is half the energy of the first.
I haven't managed to find any wrong assumption or miss-calculation.
Did anybody else catch one?
Thanks in advance - Gothican
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