A simple pendulum is made from a ping-pong ball with a mass of 10 grams, attached to a 60-cm length of thread with negligible mass. The force of air resistance on the ball is Fair =−b𝑥̇, in which = 0.016 kg s-1 [gravitational acceleration, g = 9.81 ms-2]
(a) Show that the pendulum is underdamped. Find the angular frequency, ω and the period, T of oscillation, (b) How long does it take for the amplitude of the pendulum’s swing to decrease by a factor of 1000? (c) If a pendulum made with the same ping-pong ball were to be critically damped by air resistance, what would its length have to be?
(d) An external harmonic force, F(t) = Fo cos(ωt), is applied to the ping-pong pendulum of to keep it swinging despite the air resistance. What driving angular frequency and force amplitude, Fo are required if the pendulum is to have its natural period (T0= 2π/ω0) and angular amplitude of 10o in the steady state?
1 answer
babi