For transverse vibrations, Ση,u = 0 = --------- mayı + m by2 + 2y3 = 0 -(B1) Ση,roxu = 0 (2) al a 0) --(B2) Y1 = y3, sym

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For transverse vibrations, Ση,u = 0 = --------- mayı + m by2 + 2y3 = 0 -(B1) Ση,roxu = 0 (2) al a 0) --(B2) Y1 = y3, symmetric with respect to y2 (total angular momentum y2 = -2m/mp)yı 4 = u= ks[(41 –22)+(43–42)?; T3 mavi 1= +ਨੂੰ+ਆ mavi+mguź+ mais 1 1 .2 The Lagrangian looks like, 1 2MB L=ma(ji+yą) + movi- ka[(41–42)+(43–4277 -kal -(B3) Home Work #7 (Due May 19, noon) 1) Express the Lagrangian using yı only (without yz or yz). And get the Lagrangian equation for yi, then get the expression for the angular frequency w tr. ayi dal al 2) Get the three Lagrangian equations : = 0 (for y; = 41, 42, 43 ). dt ay: From the characteristic equation (determinant of the coefficients should be zero), get the eigen values and normal modes.