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 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 ??

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