My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 6th, 2016, 08:46 AM   #1
Newbie
 
Joined: Dec 2016
From: United States

Posts: 5
Thanks: 0

Amplitude and frequency of forced square waves

I'm working on two similar problems, both with a forced square wave.

For both equations, f(t) is as follows
$\displaystyle f(t) = u(t) + 2 * sum[ (-1)^k * u(t-k*pi) ]$ , k from 0 to inf

The first asks for the amplitude of a DAMPED, FORCED square wave.
The equation is
$\displaystyle y'' + 0.1y' + y = f(t)$

I know that the solution to this ODE is
$\displaystyle y = 1 - e^(-.05t)*cos(sqrt(.9975)t) - (.05/sqrt(.9975)t)*e^(-.05t)*sin(sqrt(.9975)t) + 2* sum[ (-1)^k * u(t-k*pi)*(1-e^(-.05(t-k*pi))*cos(sqrt(.9975)*(t-k*pi)) - (.05/sqrt(.9975)*e^(-.05(t-k*pi))*sin(sqrt(.9975)*(t-k*pi))$

I have been trying to use the equation to solve for amplitude but am unsure what to plug in for F0, or if this is even the correct approach.
$\displaystyle R = F0 / (gamma*w0*sqrt(1-(gamma^2/4mk)))$, where gamma = 0.1, w0 = 1, m = 1, k = 1.



The second question asks for the slow and fast frequency (there are beats) of an UNDAMPED, FORCED square wave.
The equation is
$\displaystyle y'' + y = f(t)$

The solution to this ODE is
$\displaystyle y = 1 - cos(t) + 2 * sum( (-1)^k * u(t-11k/4) * (1-cos(t-11k/4)$

From the plot I have estimated the slow frequency to be 14 pi and the fast frequency to be 2 pi. I know that slow f = $\displaystyle abs(w-w0)/2$ and fast f = $\displaystyle abs(w+w0)/2$, but I am unsure what to plug in for each omega. Would it be correct that the forced frequency $\displaystyle w0$ would be 11/4?

Last edited by lcollins19; December 6th, 2016 at 08:49 AM.
lcollins19 is offline  
 
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
amplitude, forced, frequency, square, waves



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Laplace transform of a forced square wave lcollins19 Differential Equations 8 December 5th, 2016 04:50 PM
Fourier dB vs amplitude spectrum difference Zajja Real Analysis 1 December 3rd, 2015 07:41 PM
Amplitude of a complex number happy21 Complex Analysis 6 October 25th, 2015 08:59 AM
amplitude of a sinusoid suzuki Real Analysis 0 April 30th, 2012 08:49 PM
Determining the maximum amplitude bakslashr Algebra 0 May 17th, 2007 07:57 PM





Copyright © 2017 My Math Forum. All rights reserved.