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6. Damped simple harmonic oscillator In this part we will investigate the response of a damped simple harmonic oscillator to a driving force. The problem to solve is + + 4y = cos(wx) dx² dx where w is a positive real constant and x and y are real (non complex) variables. Question 7 Work out the analytic solution to equation (6) for the initial conditions: y Show that, for large values of x, the solution can be approximated by y = A, cos(wx+0s) d = 0 at x = 0. and write down an expression for the steady state phase 4, and for the steady state amplitude A, in terms of w. (6)

6. Damped simple harmonic oscillator In this part we will investigate the response of a damped simple harmonic oscillator to a driving force. The problem to solve is + + 4y = cos(wx) dx² dx where w is a positive real constant and x and y are real (non complex) variables. Question 7 Work out the analytic solution to equation (6) for the initial conditions: y Show that, for large values of x, the solution can be approximated by y = A, cos(wx+0s) d = 0 at x = 0. and write down an expression for the steady state phase 4, and for the steady state amplitude A, in terms of w. (6)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6. Damped simple harmonic oscillator In this part we will investigate the response of a damped simple harmonic oscillator to a driving force. The problem to solve is + + 4y = cos(wx) dx² dx where w is a positive real constant and x and y are real (non complex) variables. Question 7 Work out the analytic solution to equation (6) for the initial conditions: y Show that, for large values of x, the solution can be approximated by y = A, cos(wx+0s) d = 0 at x = 0. and write down an expression for the steady state phase 4, and for the steady state amplitude A, in terms of w. (6)
Transcribed Image Text:6. Damped simple harmonic oscillator In this part we will investigate the response of a damped simple harmonic oscillator to a driving force. The problem to solve is + + 4y = cos(wx) dx² dx where w is a positive real constant and x and y are real (non complex) variables. Question 7 Work out the analytic solution to equation (6) for the initial conditions: y Show that, for large values of x, the solution can be approximated by y = A, cos(wx+0s) d = 0 at x = 0. and write down an expression for the steady state phase 4, and for the steady state amplitude A, in terms of w. (6)
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