find the normal mode angular frequencies of the system shown below. consisting o

Question

find the normal mode angular frequencies of the system shown below. consisting of two unequal masses, with mass m and 2m, and three identical springs constant k. the masses slide on a frictionless surface. it should be possible to write each normal mode angular frequency as a numerical constant times o, where o = (k/m)1/2

find the normal mode angular frequencies of the system shown below. consisting of two unequal masses, with mass m and 2m, and three identical springs constant k. the masses slide on a frictionless surface. it should be possible to write each normal mode angular frequency as a numerical constant times ?o, where ?o = (k/m)1/2

Explanation / Answer

let x and y be displacement (from equilibrium) of the two masses to the right. we have. m*x''=-x*k+(y-x)*k. 2m*y''=-y*k+(x-y)*k. so that x''=-2xk/m+ky/m 2y''=-2yk/m+kx/m. w0=sqrt(k/m) so that x''=-2*xw0^2+y*w0^2. 2y''=-2*y*w0^2+x*w0^2. let x=A*e(iwt) and y=B*e(iwt). then plug x and y into the equation to get w1 and w2 out.

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