About the formula of pendulum -- What if there is damping?

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karimce
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http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple

a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

a(t) : the angle in instant t .
t : time
g : gravity .
Pi = 3.14
k = Fixed (Friction )
l : longer of pendulum

but this formula is wrong , because the curve of this formula Remains constant , like this :
K9i9f.png


I want to correct this equation to become true Means keeps decreasing curve, even non-existent ( = 0 ) .
lwTAG.png

Specifically I want to change in the second part , in [ k/(m*l*l) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

can you help me ? Are there any other equation?
 
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