Physics218sol1 - PHYS 218 - SOLUTION TO ASSIGNMENT 1 02 Feb...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYS 218 - SOLUTION TO ASSIGNMENT 1 02 Feb 2007 By Eliot Kapit and Chung Koo Kim e-mail : ek359@cornell.edu and ck269@cornell.edu 1. Damped Harmonic Motion (a) Quite obviously, this is a damped pendulum; the factor of exp- . 25 t indicates that the oscillation will decay with time. (b) See graph: (c) We can extract the damping, = 2 * . 25 = 0 . 5 s- 1 , the oscillation frequency b = 12 s- 1 , the natural frequency = p b 2 + 2 / 4 = 37 . 7 s- 1 and the initial phase shift = 3. One cannot measure the mass since the acceleration from gravity is independent of it, and terms such as and F all depend on the existence of a driving force, which is not present in this problem. (d) T = 2 / = 1 / 6. The other characteristic time is the decay constant = 1 / . 25 = 4 s , which is the time it would take for the amplitude to decay by a factor of 1 /e . 2. Effect of gravity on a hanging spring (a) One arrow pointing down, and another one up, representing weight (= mg ) and restoring force of spring ( = k ( l- l )), respectively. (Diagram omitted) (b) From Newtons 2nd law for vertical direction, mg- k ( l- l ) = 0, or l = l + mg k 1 (c) If the mass is pulled down by y from the new equilibrium, we get, from...
View Full Document

Page1 / 3

Physics218sol1 - PHYS 218 - SOLUTION TO ASSIGNMENT 1 02 Feb...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online