课程名称︰力学上 课程性质︰系必修 课程教师︰陈俊玮 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2008/11/07 00:00am 公布试题 考试时限（分钟）：to 2008/11/17 10:20am (take-home examination) 是否需发放奖励金： （如未明确表示，则不予发放） 试题 : You can send me e-mails ([email protected]) for questions. I will answer them on the course website. But because of my travel, I probably won't answer your questions as soon as I would like to. 1) (20 points) Redo example 3.7 (p.136) of the text book but with different initial conditions: x(t = -1/γ) = 0 and x'(t = -1/γ) = F0/(m*ω1). 2) (20 points) Double pendulum problem: see the configuration in http://scienceworld.wolfram.com/physics/DoublePendulum.html (This webpage will be linked on the course website, too.) (a) Derive the equations of motion using Newton's second law rether than using the variational approach as shown in the above webpage. Compare your equations with Eqs. (14)＆(19) of the above webpage. (b) Draw plots (you may use computer to do so) similar to those in page 167 of the textbook: please draw θ1 vs t, θ1' vs θ1, the Poincare section, and θ2 vs t ,θ2' vs θ2 and Poincare section for (i) θ1 = 0, θ2 = π/2 (ii) θ1 = π/2, θ2 = 0 (iii) θ1 = π/2, θ2 = π/2, while θ1' = θ2' = 0 in all the cases. We will work in special units such that m1 = m2 = 1, l2 = 2*l1 = 1, g = 1. (If you cannot derive the equations of motion, you can use Eqs.(14)＆ (19) of the above webpage to make those plots.) 3) (20 points) Do problem 4-22 of page 181. 4) (20 points) Try to understand Figure 4-14, 4-15 and 4-16 by solving the equation (you may use a computer to do so) m*x" = -γ*x' + F(x) + F0*cos(w*t), with F(x) defined in Eq.(4.37). 5) (20 points) Calculate the effect of the Sun to tides on Earth, using the same approximations as those in section 5.5. Explain, by explicit calculations, (a) The highest tides occur when Earth, the Moon, and the Sun are lined up. (b) The smallest tides occur for the first and third quarters of the Moon when the Sun and Moon are at right angles. (c) The maximum tide, which occurs every 2 weeks, should be 0.83m for the spring tides. (This is the first paragraph after example 5.5.) --

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