# differential equation

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A simple pendulum of length is oscillating through a small angle θ in a medium for which
the resistance is proportional to the velocity. Obtain the differential equation of its motion
and discuss the motion.

• differential equation -

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.

• differential equation -

• differential equation -

d^2theta/dt^2 +(g/l)sin(theta)=0

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