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Tham khảo tài liệu 'classical mechanics - 3rd ed. - goldstein, poole & safk episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 268 Chapter 6 Oscillations FIGURE 6.7 Dependence of the angular velocity i dộ dt on the time for an applied torque N Nc. The average value a increases linearly with time in the absence of damping linear region and the overall curve applies to the case a e too with damping. value of the applied torque. When this occurs the average angular speed to approaches a limiting value to as shown in Fig. 6.7 and the acceleration fluctuates around an average that is zero dt2 0. The pendulum undergoes what is called quasi-static motion rotating with an angular speed to that undergoes periodic variations but always remains close to the average l. To obtain more insight into this quasi-static behavior we neglect the acceleration term in the equation of motion 6.92 and write N N c 1 dộ 77 sin ự toc dt 6.97 which is an equation that can be solved analytically with the solutions to 0 to wt m 2-1 1 2 to N Nc a c for N Nc for V Nc for N Nc 6.98a 6.98b 6.98c which are plotted in Fig. 6.8. The actual cyclic variations in to for points A and B on this plot are presented in Fig. 6.9. At point A the applied torque has the value N 1.2TVC so from Eqs. 6.95 the net torque varies between 0.2Nc and 2.27VC around the cycle and the angular speed is fast at the bottom and slow at the top with the variations shown at the lower part of Fig. 6.9. For point B we have TV 2NC so the net torque varies between Nc and 3NC producing the more regular variations in angular speed presented 6.6 The Damped Driven Pendulum and the Josephson Junction 269 FIGURE 6.8 Relationship between the applied torque N and the average angular velocity a for 1 C g ŨỊ . We see that ft 0 for N Nc and increases with increasing N Nc. FIGURE 6.9 Oscillations at points A V Ỉ.2NC and B 2 Vr for a c CD indicated on Fig. 6.8 for the damped harmonic oscillator. Adapted from A. Barone and G. Patemo Physics and Applications of the Josephson Effect Wiley NY 1982. 270 Chapter 6 Oscillations at the top of Fig. 6.9. In the limit N Nc meaning a
