Question

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.

Answer 1

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.

Answer 2

is that true answer?

Answer 3

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

Answer 4

Yes