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Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 271

8.21. Pars, L. A., A Treatise on Analytical Dynamics, Ox Bow Press, Wood Bridge, CT, 1979.
8.22. Goldstein, H., Classical Mechanics, Addison-Wesley, Reading, MA, 1980.
8.23. Kane, T. R., and Levinson, D. A., Formulations of equations of motion for complex spacecraft,
J. Guidance Control, 3(2), 99–112, 1980.
8.24. Beer, F. P., and Johnston, Jr., E. R., Vector Mechanics for Engineers, McGraw-Hill, New York, 1984.
8.25. D’Souza, A. F., and Garg, V. K., Advanced Dynamics Modeling and Analysis, Prentice Hall,
Englewood Cliffs, NJ, 1984.
8.26. Torby, B. J., Advanced Dynamics for Engineers, Holt, Rinehart & Winston, New York, 1984.
8.27. T.R. Kane, T. R., and Levinson, D. A., Dynamics: Theory and Applications, McGraw-Hill, New
York, 1985.
8.28. Meriam, J. L., and Kraige, L. G., Engineering Mechanics, Wiley, New York, 1986.
8.29. Marion, J. B., and Thornton, S. T., Classical Dynamics of Particles and Systems, Harcourt, Brace
& Jovanovich, San Diego, CA, 1988.
8.30. Huston, R. L., Multibody Dynamics, Butterworth-Heinemann, Boston, MA, 1990.
8.31. Haug, E. J., Intermediate Dynamics, Prentice Hall, Englewood Cliffs, NJ, 1992.
8.32. Desloge, E. A., Classical Mechanics, Wiley, New York.

Problems

Section 8.4 The Simple Pendulum
P8.4.1: A simple pendulum with length of 3 ft has a speed V of 5 ft/sec when the
pendulum bob P is in its lowest position as shown in Figure P8.4.1. Find the tension T in
the support cable.

O
O
3 ft
30°
3 ft
2 ft/sec
P
5 ft/sec
FIGURE P8.4.1 FIGURE P8.4.3
A simple pendulum. An inclined simple pendulum.
P8.4.2: Repeat Problem P8.4.1 if the pendulum length is 2 m and the speed V of the bob
P is 4 m/sec.
P8.4.3: See Problem P8.4.1. Find the tension T in the support cable if the bob P has a speed
of 2 ft/sec when the pendulum inclination angle θ is 30°, as in Figure P8.4.3.
P8.4.4: See Problem P8.4.3. Find the horizontal and vertical components of the support
reactions O and O in the configuration of Figure P8.4.3.
x
y
P8.4.5: Consider Eq. (8.4.4) governing the motion of a simple pendulum:
˙˙ θ = ( ) l sinθ = 0
g