The objective is to determine the length of the pendulum so that it can swing ba
ID: 1816795 • Letter: T
Question
The objective is to determine the length of the pendulum so that it can swing back and forth with a period of one second. Although the equation dose not appear to be too complicated, it is nonlinear and cannot be solved for this simple design problem. One approach to solve the problem is to linearize the model equation around an NOP corresponding to its static equilibrium configuration.
(1)
Convert the nonlinear model to the said linear model.
(2)
Obtain the expression for the natural frequency of the system from the linear model. Neglecting the light damping, obtain the expression for the period of pendulum swing.
(3)
Determine the length of the pendulum so that the period of swing would be one second.
Explanation / Answer
1) sin
mL2" + cL2' + mgL = 0
2) neglect damping,
mL2" + mgL = 0
" + (g/L) = 0
= (g/L)
period T = 2/ = 2(L/g)
3) T = 1 s
L = g(T/2)2 = 0.248 m