課程名稱︰力學上
課程性質︰系必修
課程教師︰陳俊瑋
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2008/11/07 00:00am 公布試題
考試時限（分鐘）：to 2008/11/17 10:20am (take-home examination)
是否需發放獎勵金：
（如未明確表示，則不予發放）
試題 :
You can send me e-mails (jwc@phys.ntu.edu.tw) 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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