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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 24th, 2015, 03:47 AM #11 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra You should form your equations with only $\ddot x_n$ on the left (divide by $m_n$) to do this. Then form your matrices. January 24th, 2015, 03:51 AM #12 Newbie   Joined: Jan 2015 From: world Posts: 11 Thanks: 0 Can you make the solution? I can not do more. how find to eigen frequencies January 24th, 2015, 04:02 AM #13 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra You aren't trying! January 24th, 2015, 04:11 AM #14 Newbie   Joined: Jan 2015 From: world Posts: 11 Thanks: 0 I'm trying to do, but it is not. Show route. January 24th, 2015, 05:03 AM #15 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra We have \begin{aligned}&& m_1 \ddot x_1 &= k_1(x_2 - x_1) - k_2x_1 \\ && 2\ddot x_1 &= 2x_2 - 3x_1 \\ && \ddot x_1 &= x_2 - \tfrac32 x_1 \\ &\text{similarly} & \ddot x_2 &= \tfrac12 x_1 - \tfrac34 x_1 \end{aligned} Now we assume that $x_n =a_n \mathrm e^{\mathrm i \omega t}$ so that $\ddot x_n = -\omega ^2 x_n$. You can now eliminate $\ddot x_n$ from the equations and form an eigenvalue matrix problem. January 24th, 2015, 09:03 AM #16 Newbie   Joined: Jan 2015 From: world Posts: 11 Thanks: 0 I could not solve my teacher. I'm trying, but no solution. Can you solve it? Although a little way then you are here. January 24th, 2015, 09:52 AM #17 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra \begin{aligned} &\text{We have} & \ddot x_1 &= x_2 - \tfrac32 x_1 \qquad \ddot x_1 = -\omega^2 x_1 \\ &\text{so} & -\omega^2 x_1 &= x_2 - \tfrac32 x_1 \implies (\omega^2 - \tfrac32)x_1 + x_2 = 0 \end{aligned} You can do the same for $\ddot x_2$. Then you can make a matrix equation $Ax = 0$ who CH means that the determinant of A is zero. That gives an equation which you can solve for $\omega$. January 24th, 2015, 10:57 AM #18 Newbie   Joined: Jan 2015 From: world Posts: 11 Thanks: 0 Is the right solution? 1) 2) 3) Last edited by yakamoz29; January 24th, 2015 at 11:12 AM. January 25th, 2015, 10:39 AM #19 Newbie   Joined: Jan 2015 From: world Posts: 11 Thanks: 0 result w1,2=+-34,9 ?? Tags differential, equations, matrix, question 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 MadSoulz Differential Equations 1 January 27th, 2014 08:52 AM rishav.roy10 Differential Equations 0 August 21st, 2013 05:59 AM erre Differential Equations 2 April 9th, 2012 06:58 AM derekking Linear Algebra 3 February 25th, 2012 01:25 AM by_dj_omar Differential Equations 3 May 22nd, 2011 12:57 PM

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