I hope that the two components of the velocity of m2 that I have marked are self-explanatory; the speed of m2 is given by \( v^2_{2} = l^2_{1}\dot{\theta}^2_{1} + l^2_{2}\dot{\theta}^2...I hope that the two components of the velocity of m2 that I have marked are self-explanatory; the speed of m2 is given by v22=l21˙θ21+l22˙θ22+2l1l2˙θ1˙θ2cos(θ2−θ1). Equating the two expressions for the ratio θ2/θ1, or putting the determinant of the coefficients to zero, gives the following equation for the frequencies of the normal modes:
