# Homework #2

*Due Friday of Week 2 at 5pm*

**1.** Turn in your computer program that solves v' = -g + αv². The program should have comments that keep track of units. You should include a graphical representation of the solution (graphs need a title, axis labels and axis units) and evidence that your time step is small enough to get an accurate answer.

**2.** From Mahajan text book: Problems 1.1, 1.4, 1.5, 1.12

**3.** In class we used complex numbers to elegantly solve the damped-driven harmonic oscillator. Using the class notes as a starting point, derive an expression for the phase difference between the driving force and the motion.

**4.** Using the Green's function approach, find the amplitude of motion when a damped-driven harmonic oscillator is driven at it's resonant frequency. Assume that the damping term is small α « ω_0.

*Points allocation: 1) 6pts, 2) 4pts, 3) 3pts, 4) 7pts.*