Page 500 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 14 Problems 487

Figure P14-38.
14-39 For a given value of g//, determine the frequencies of the excitation for which the
simple pendulum of Prob. 14-38 with a stiff arm / will be stable in the inverted
position.
14-40 Determine the perturbation solution for the system shown in Fig. P14-40 leading to a
Mathieu equation. Use initial conditions i(0) = 0, x(0) = A.

Figure P14-40.

14-41 Using the Runge-Kutta routine and g/l = 1.0, calculate the angle 6 for the simple
pendulum of Prob. 14-29.
14-42 With damping added to Prob. 14-41, the equation of motion is

0 + 0.300 F sin 0 ^ 0
Using the Runge-Kutta method, solve for the initial conditions 0(0) = 60°, 0(0) = 0.
14-43 Obtain a numerical solution for the system of Prob. 14-40 by using (a) the central
difference method and (b) the Runge-Kutta method.