1. find the phase space of the harmonic oscillator
x_double_dots + (w^2)x = 0
and the one parameter group of diffeomorphisms gt . also find two different
type of orbits. are these orbits phase curves?
2. consider the nonlinear pendulum
x_double_dots + sin(x) = 0
describe four different types of phase curves for the nonlinear pendulum.

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

Two polarizers are oriented at 40∘ to each other and plane-polarized light is incident on them. if only 16 percent of the light gets through both of them, what was the initial polarization direction of the incident light?

Apotter's wheel moves uniformly from rest to an angular speed of 0.20 rev/s in 32.0 s. (a) find its angular acceleration in radians per second per second. rad/s2 (b) would doubling the angular acceleration during the given period have doubled final angular speed?