Florida State University
Department of Physics
PHY 5246
Assignment # 2 (Due Friday, September 18th, 2009)
(1) (10 points) Fetter and Walecka 1.12
(2) (10 points) Fetter and Walecka 1.14
(3) (10 points) Fetter and Walecka 1.15. Note that parts (c) and (d)
Florida State University
Department of Physics
PHY 5246
Assignment # 1 (Due Wednesday, September 9th, 2009)
(1) (10 points) A massless string is placed over a masssless pulley, and each end is wound
around and fastened to a vertical hoop. The hoops have m
Florida State University
Department of Physics
PHY 5246
Assignment #3 (Due Monday, October 5th, 2009.)
(1) (10 points) A particle of unit mass is released from rest at a point of latitude , and falls
under gravity in a medium which produces a retardation
Florida State University
Department of Physics
PHY 5246
Assignment # 4 (Due Friday, 23rd October, 2009)
(1) (10 points) If L is a Lagrangian for a system of n degrees of freedom satisfying Lagranges
equations, show by direct substitution that
L = L +
dF (
Florida State University
Department of Physics
PHY 5246
Assignment # 5 (Due Wednesday, 4th November, 2009)
(1) (10 points) (a) A block sits on a frictionless plane inclined at an angle with the
horizontal. The block is free to slide down the plane. Using
& Coordinate of Center mass : ( x, y ) Velocity of CM ( x, y ) & Acceleration ( &, &) xy Lagrangian (Rotation w.r.t. CM frame) : L= 1 1 1& & & Mx 2 + My 2 + I 2 Mgy 2 2 2
L 2
L x 2 cos = 0 with constraints : L y sin = 0 2
I=
2 x dx = L 2
x 3
3
L 2 L 2
=
Florida State University
Department of Physics
PHY 5246
Assignment # 6 (Due Friday, 20th November, 2009)
(1) (15 points) Fetter and Walecka 4.9. If you show that the secular equation has three
degenerate modes at 2 = 0 using Mathematica, Maple, or similar