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 December 6th, 2016, 07:46 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 07:49 AM. Tags amplitude, forced, frequency, square, waves Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lcollins19 Differential Equations 8 December 5th, 2016 03:50 PM Zajja Real Analysis 1 December 3rd, 2015 06:41 PM happy21 Complex Analysis 6 October 25th, 2015 08:59 AM suzuki Real Analysis 0 April 30th, 2012 08:49 PM bakslashr Algebra 0 May 17th, 2007 07:57 PM

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