A pendulum of length L oscillates in a vertical plane. Assuming that the mass of the pendulum is all concentrated at the end of the pendulum, show that it obeys the differential equation

where g is the acceleration due to gravity and Ï• is the angle between the pendulum and the vertical. This equation cannot be solved exactly. For small oscillations such that

sin (Ï•) ‰ˆ Ï•,

find the solution to the equation. What is the period of the motion? What is the frequency? Find the value of L such that the period equals 2.000 s.

Transcribed Image Text:

´d²p> = -g sin (ø), df2