Reference no: EM131787236
Question - Given the equation of motion of a 2-DOF system:
J1θ¨1(t) + 2ktθ1(t) - ktθ2(t) = 0
J2θ¨2(t) + 2ktθ1(t) + 2ktθ2(t) = 0
(1) Rewrite them into matrix form:
(2) From above matrix form, define the coefficient matrix of 
as J, define the coefficient matrix of 
as K, define θ = , We will have a simplified matrix of form: _____.
In order to have non-zero solution, we need det (-ω2J + K) = 0, express that in its detailed matrix form.
(3) Given J1 = J2 = 1 kg.m2, kt =1 N.m/rad, find the natural frequencies ω1 and ω2.
(4) Given J1 = J2 = 1 kg.m2, kt = 1N.m/rad, find the amplitude ratio r1 and r2.