# Homework #1, 2013

*Due on Day 3: Wednesday at 5pm*

## Q1 Read a research article related to the class

Read the journal club assignment

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?

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.