A simple pendulum is set into oscillation from its rest position
by giving it an angular velocity of 1 rad/s. It is found to
oscillate with an amplitude of 0.5 rad. Find (a) the natural
frequency ωn and (b) the length l of the pendulum. To do so, draw
the FBD, derive the equation of motion, solve for the expression
for the natural frequency, and apply the initial conditions to the
general solution of the equation of motion. (Note: this system
is undamped.)
Ans. a) natural frequency ωn = 2 rad/s b) pendulum length l ≈
2.45 m