A simple pendulum of length l is oscillating through a small angle in a medium in which the resistance is proportional to the velocity. Find the differential equation of its motion. Discuss the motion and find the period of oscillation.
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ML d^2è/dt^2 + k*L*dè/dt + Mg è = 0
or
d^2è/dt^2 + (k/M)*dè/dt + (g/L) è = 0
k is the damping constant of proportionality (force/velocity)
The solution is damped harmonic motion.
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