Solnmt1(1) - Physics 315 Oscillations and Waves Midterm 1 Solutions 1(a ω is the characteristic angular oscillation frequency of the system(b The

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: Physics 315: Oscillations and Waves Midterm 1: Solutions 1. (a) ω is the characteristic angular oscillation frequency of the system. (b) The characteristic frequency in cycles per second is f = ω/ 2 π . (c) x ( t ) = x cos( ω t ). (d) Now, d E dt = 2 ˙ x ¨ x + 2 ω 2 x ˙ x, or d E dt = 2 ˙ x ( ¨ x + ω 2 x ) . However, ¨ x + ω 2 x = 0. Hence, d E /dt = 0. E is twice the energy per unit mass of the system. 2. (a) ν parameterizes the amount of damping in the system. (b) If x ( t ) = A sin( ω 1 t ) e γ t then ˙ x ( t ) = A ω 1 cos( ω 1 t ) e γ t + A γ sin( ω 1 t ) e γ t , and ¨ x ( t ) =- A ω 2 1 sin( ω 1 t ) e γ t +2 A ω 1 γ cos( ω 1 t ) e γ t + A γ 2 sin( ω 1 t ) e γ t . Hence, substitution into the damped harmonic oscillator equation yields 0 = bracketleftbig ω 2- ω 2 1 + γ ν + γ 2 bracketrightbig sin( ω 1 t ) + [2 γ ω 1 + ν ω 1 ] cos( ω 1 t ) ....
View Full Document

This note was uploaded on 10/04/2011 for the course PHY 315 taught by Professor Staff during the Spring '08 term at University of Texas at Austin.

Page1 / 3

Solnmt1(1) - Physics 315 Oscillations and Waves Midterm 1 Solutions 1(a ω is the characteristic angular oscillation frequency of the system(b The

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