(a) For a coupled oscillator shown in the figure below, write down the equations of motion...

 

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(a) For a coupled oscillator shown in the figure below, write down the equations of motion under the conditions of small deflections and no damping. (b) Obtain the corresponding equations in a matrix form and write down the expressions for the mass and stiffness matrices M and X, respectively. (c) Obtain the eigenvalues and eigenvectors and interpret the results. (d) Show that | e₁> are the eigenvectors in the 'bra-ket' notation. [5] wamewwwwww 2k mm a 2k jaythakur (a) For a coupled oscillator shown in the figure below, write down the equations of motion under the conditions of small deflections and no damping. (b) Obtain the corresponding equations in a matrix form and write down the expressions for the mass and stiffness matrices M and X, respectively. (c) Obtain the eigenvalues and eigenvectors and interpret the results. (d) Show that | e₁> are the eigenvectors in the 'bra-ket' notation. [5] wamewwwwww 2k mm a 2k jaythakur