Homework Set 1
Due: Wednesday, September 5, 2012
1.
Consider a vibrating star, whose frequency depends (at most) on its radius R, mass density , and
Newtons gravitational constant G. How does depend on R, , and G?
2.
A particle with mass m and initial spe
Homework Set 2
Due: Friday, September 14, 2012
1.
Consider a rocket subject to a linear resistive force, f = bv , but no other external forces. Show that if
the rocket starts from rest and ejects mass at a constant rate k = m, then its speed is given by
v
Homework Set 3
Due: Wednesday, September 26, 2012
1.
Let x1 (t) and x2 (t) be solutions to x2 = bx. Show that x1 (t) + x2 (t) is not a solution to this equation.
2.
A mass on the end of a spring (with natural frequency ) is released from rest at position
Homework Set 4
Due: Monday, October 8, 2012
1.
Find the Fourier coecients an and bn for the function shown below.
fmax
0
1
2
3
4
Using Mathematica, make a plot comparing the function itself with the rst couple of terms in the Fourier
series, and another f
Homework Set 5
Due: Wednesday, October 31, 2012
1.
Argue that if it happens that the integrand f (y, y , x) does not depend explicitly on x, that is f = f (y, y ),
then
df
f
f
=
y + y .
dx
y
y
Use the Euler-Lagrange equation to replace f /y on the right,