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##E = \frac{1}{2}(kx^2+m \dot{x}^2)##
## \frac{2E - kx^2}{m}=\dot{x}^2##
##\frac{dx}{dt} = \sqrt{\frac{2E - kx^2}{m}}## or ## dt = \sqrt{\frac{m}{2E - kx^2}}dx ## ⇒##= \frac{1}{\sqrt{\frac{2E - kx^2}{m}}}dx##
My Question please help me.
1. I know ##T = 2\pi\sqrt{\frac{m}{k}} .## but i don't understand why ##T = 2 \int_{-l}^{l}\frac{1}{\sqrt{\frac{2E - kx^2}{m}}}dx##2.In this case. Why do we choose the probability density function, ## p(x) = \frac{2dt}{T} ## ?