?BC,
Then you have answered your problem as stated in your original post:
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"Here's my prob. Using the kinematic equations for constant acceleration
etc. I fond the formula for speed at BDC (and the work-energy principle)
X dot = sqrt.(g*L) A as a means of measuring the amplitude.
I obtain the same formula by using the total energy of the P. using 0.5(M
L^2 * theta dot) and m*g*h h = L(1-cos(theta) and using E = PE at the max
deflection (amplitude). However, and this is my prob. To obtain the same
equation I must use the approximation cos =~ 1 - theta^2 / 2!"
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The equation X dot = sqrt.(g*L) A already has the small angle approximation
{cos =~ 1 - theta^2 / 2} built into it.
So the exact equation will only match it if it (the exact equation) is also
given the small angle approximation.