PHY 711 Classical Mechanics

Show how the solution given in Eq. 12.15 approximately solves the differential equation for the Foucault pendulum given in Eq. 12.7. Estimate the period of rotation for a pendulum located in Winston-Salem.

PHY 711 -- Assignment #6

September 6, 2006

Continue reading Chapter 2 in Fetter & Walecka.

Consider the brachistochrone integral (17.7) of your text, with x₁=0, x₂=πa, y₁=2a, and y₂=0. Evaluate the integral for the following two cases:
1. x(θ)= a(θ – sin(&theta) )
  y(θ)= a(1 + cos(&theta))
  0 ≤ θ ≤ π
2. y(x) = 2a – (2/π) x
  0 ≤ x ≤ πa

PHY 711 -- Assignment #7

September 8, 2006

Continue reading Chap. 3 Fetter & Walecka.

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PHY 711 -- Assignment #8

September 13, 2006

Continue reading Chap. 3 Fetter & Walecka.

Work problem 3.5 in Fetter & Walecka.

PHY 711 -- Assignment #9

September 15, 2006

Continue reading Chap. 3 Fetter & Walecka.

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PHY 711 -- Assignment #10

September 18, 2006

Start reading Chapter 6 in Fetter & Walecka.

Work problem #6.18 in Fetter & Walecka.

PHY 711 -- Assignment #11

September 22, 2006

Continue reading Chapter 6 in Fetter & Walecka.

Read Section III of the paper by Hans C. Andersen on Molecular Dynamics Simulations. Work through the steps to derive the Hamiltonian function in Eq. 3.6 from the Lagrangian function in Eq. 3.2 of that paper.

PHY 711 -- Assignment #12

September 25, 2006

Finish reading Chapter 6 in Fetter & Walecka.

Consider the Hamilton-Jacobi equations presented in Section 35 of your text. Find the trajectory q(t) and S(q,α,t) for the example:
V(q) = mg q,
where g is the constant gravitational acceleration and the potential represents that of a constant gravitational potential, with q(t) representing the vertical displacement.

PHY 711 -- Assignment #13

September 26, 2006

Start reading Chapter 4 in Fetter & Walecka.

Work problem #4.2 in Fetter & Walecka.

PHY 711 -- Assignment #14

October 9, 2006

Continue reading Chap. 5 Fetter & Walecka.

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PHY 711 -- Assignment #15

October 16, 2006

Finish reading Chapter 5 in Fetter & Walecka.

Work problem #5.10 in Fetter & Walecka.

PHY 711 -- Assignment #16

October 18, 2006

Start reading Chapter 9 in Fetter & Walecka.

Consider Eq. 48.14 in Fetter & Walecka. Write out the expressions in cartesian coordinates and convince yourself that the identity is correct.

PHY 711 -- Assignment #17

October 20, 2006

Continue reading Chapter 9 in Fetter & Walecka.

The above photo shows a syringe with a liquid (density ρ=1000 kg/m³ ) inside the barrel (cross sectional area 8 x 10^-5 m²). Suppose a force of F = 1 N is applied to the barrel. What is the velocity of the liquid coming out of the needle (cross sectional area 8 x 10^-7 m²)?