Question

 If two pendulums each of mass 0.6 kg and length 1m are connected by a spring of force constant 0.3 

N/m, calculate the normal modes of frequencies for the coupled system.

Answer 1

$$\omega_1=\sqrt{\frac{g}{l}}=\sqrt{\frac{9.8}{1}}=3.13\frac{rad}{s}$$

$$\omega_2=\sqrt{\frac{g}{l}+\frac{2k}{m}}=\sqrt{\frac{9.8}{1}+2\frac{0.3}{0.6}}=3.28\frac{rad}{s}$$

$$f_1=\frac{3.13}{2\pi}=0.498\ Hz\\f_2=\frac{3.28}{2\pi}=0.52\ Hz$$