Transcription of Chapter 24 Physical Pendulum
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Chapter 24 Physical Pendulum
Chapter 24 Physical Pendulum Introduction .. 1 Simple Pendulum : Torque Approach .. 1 Physical Pendulum .. 2 Worked Examples .. 4 Example Oscillating Rod .. 4 Example Torsional Oscillator .. 7 Example Compound Physical Pendulum .. 9 Appendix 24A Higher-Order Corrections to the Period for Larger Amplitudes of a Simple Pendulum .. 12 24-1 Chapter 24 Physical Pendulum .. I had along with Descriptions, with some Drawings of the principal Parts of the Pendulum -Clock which I had made, and as also of them of my then intended Timekeeper for the Longitude at John Harrison Introduction We have already used Newton s Second Law or Conservation of Energy to analyze systems like the spring-object system that oscillate. We shall now use torque and the rotational equation of motion to study oscillating systems like pendulums and torsional springs. Simple Pendulum : Torque Approach Recall the simple Pendulum from Chapter coordinate system and force diagram for the simple Pendulum is shown in Figure (a) (b) Figure (a) Coordinate system and (b) torque diagram for simple Pendulum The torque about the pivot point P is given by P= rP,m m g=l r mg(cos r sin )= lmgsin k ( ) The z-component of the torque about point P ( P)z= mglsin.
A physical pendulum consists of a uniform rod of length d and mass m pivoted at one end. The pendulum is initially displaced to one side by a small angle θ 0 and released from rest with θ 0 <<1. Find the period of the pendulum. Determine the period of the pendulum using (a) the torque method and (b) the energy method. Figure 24.3 Oscillating rod
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