# Homework #1, 2013

Due on Day 3: Wednesday at 5pm

## Q1 Read a research article related to the class

Find an article with an appropriate topic that was published in a listed journal.

Read the article. Write down the first author, article title, journal name, journal volume, page number and year of the article. Write a one paragraph summary of the article.

Note: This question will be repeated in HW#2 and HW#3 so that you become familiar with at least three different articles.

## Q2: Two coupled electrical oscillators

a) Find a pair of coupled differential equations that describe the time dependent behavior of the circuit in Fig. 1. Solve these coupled differential equations to find the natural frequencies of the system.

b) One of the natural frequencies is independent of C' – discuss the physical significance of this (what does the pattern of charge motion look like?).

c) If C' » C, and the correct initial conditions are chosen, charge in the right-side of the circuit will oscillate while gradually transferring energy to the left-side of the circuit. What initial conditions would generate this behavior?

 Figure 1

Suggested approach for part a):

• First, solve the simplest system with one capacitor and one inductor. This will remind you how to describe circuit dynamics in terms of charge on a capacitor plate and the sum of the voltages in a loop.
• Second, analyze Fig. 1 in terms of charge on leftmost capacitor, and charge on the rightmost capacitor.