3. Consider two coupled oscillators whose equations of motion are given by d'z = -3r + , dr? = - 3r2, dr2 (a) Calculate the characteristic determinant for this system. Note: The characteristic determinant is det M-1, where M is the matrix for which x+Mx = 0 and 2 is the normal mode frequency. (b) Compute the frequencies of the normal modes of oscillation. (c) Solve the cquations of motion subject to the initial conditions z (0) 0.02 m, z(0) -0.02 m. (0)--0.1 ms and i(0) = 0.1 ms.
3. Consider two coupled oscillators whose equations of motion are given by d'z = -3r + , dr? = - 3r2, dr2 (a) Calculate the characteristic determinant for this system. Note: The characteristic determinant is det M-1, where M is the matrix for which x+Mx = 0 and 2 is the normal mode frequency. (b) Compute the frequencies of the normal modes of oscillation. (c) Solve the cquations of motion subject to the initial conditions z (0) 0.02 m, z(0) -0.02 m. (0)--0.1 ms and i(0) = 0.1 ms.
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Transcribed Image Text:3. Consider two coupled oscillators whose equations of motion are given by
-3z1 +z,
dt?
d²r2
= I - 3r2,
(a) Calculate the characteristic determinant for this system.
Note: The characteristic determinant is det M-1, where M is the matrix for which x+Mx = 0
and 2 is the normal mode frequency.
%3D
(b) Compute the frequencies of the normal modes of oscillation.
(c) Solve the cquations of motion subject to the initial conditions r (0) = 0.02 m, r>(0)
(0) - -0.1 ms and (0)
(d) Show that the normal coordinates for the system are given by yh = + 2 and y2 = -2.
Use the initial conditions from (c) to find the solution in terms of the normal coordinates.
= 0.02 m.
0.1 ms
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