PHY 501 Fall 2013
Homework 1: Solutions
In each of the following problems:
(i) introduce convenient generalized coordinate(s) qj of the system.
(ii) write down the Lagrangian L as a function of q j ,
PHY 501 Fall 2013
Problems for initial self-check: Solutions
Problem 1.1. Find acceleration of a rocket due to working jet motor, and explore the resulting
equation of rockets motion.
Hint: For the sa
PHY 501 Fall 2013
Optional problems Set 1: Solutions
Problem 2.5. For the system of two pendula which was the subject of Problem 1.3:
(i) introduce convenient generalized coordinate(s) qj of the syste
PHY 501 Fall 2013
Midterm Exam: Solutions
Problem M.1 (to be graded of 900 points). A pendulum of mass m is hung on
another point mass m that may slide, without friction, along a straight horizontal r
PHY 501 Fall 2013
Homework 7: Solutions
Problem 6.3. A uniform, round disk of radius R can rotate, without
friction, in the vertical plane, about a horizontal axis A displaced by R/2 from
the disk cen
PHY 501 Fall 2013
Homework 6: Solutions
Problem 5.5 (to be graded of 40 points). Calculate and analyze the dispersion relation (k) for
longitudinal waves in an infinite 1D chain of coupled oscillators
PHY 501 Fall 2013
Homework 5: Solutions
Problem 5.1. For the system of two elastically coupled pendula,
confined to a vertical plane, with the parameters shown in Fig. on the right
(cf. Problem 1.3),
PHY 501 Fall 2013
Homework 4: Solutions
Problem 4.5 (to be graded of 20 points). Find the fixed point of the following system of
equations:
q1 q1 4q 2 ,
q 2 q1 q 2 .
Analyze its stability. What type o
PHY 501 Fall 2013
Homework 3: Solutions
Problem 4.2. A square-wave pulse of force (see Fig.
on the right) is exerted on a linear oscillator with
eigenfrequency 0 (no damping), initially at rest. Calcu
PHY 501 Fall 2013
Homework 2: Solutions
Problem 3.1. Use Eq. (3.27) of the lecture notes to calculate the functional dependence of period
T of oscillations of a 1D particle of mass m in potential U(q)
Classical Mechanics and Dynamics
PHY 501
Fall 2009
Homework 1 with solutions
In each problem of this assignment:
(i) introduce a set of convenient generalized coordinate(s) qj of the system,
(ii) writ