(a) Write down the equations of motion corresponding to (11.2) for the equal-mass carts of Section 11.2 with three identical springs, but with each cart subject to a linear resistive force by (same coefficient b for both carts) and with a driving force F (t) = Fo cos cot applied to cart 1. (b) Show that if you change variables to the normal coordinates 1 = 1(x1 + x2) and 2 = z (x1 x2), the equations of motion for ci and b2 are uncoupled. (c) Using the methods of Section 5.5, write down the general solutions. (d) Assuming that /3 = b/2m << coo, show that i resonates when co ti coo = Oclm and likewise b2 when co tiNijcoo. (e) Prove, on the other hand, that if both carts are driven in phase with the same force Fo cos cot, only i shows a resonance. Explain. Figure 11.16 11.12

Astronomy 103 Week 3 Friday class last week was Activity Worksheet #6 10/3/2016 Homework due Wednesday Exam on Friday, multiple choice Kepler’s laws describe how planets revolve around the Sun. Not why. His laws are observational. What do we need to describe why one object revolves around another • Gravity • Observation tells us that objects interact...