(Solved): 2DOF system as shown in figure below, M1 \( =4 \mathrm{~m}, \mathrm{M} 2-8 \mathrm{~m}, \mathrm{kl} ...

2DOF system as shown in figure below, M1 \( =4 \mathrm{~m}, \mathrm{M} 2-8 \mathrm{~m}, \mathrm{kl}-5 \mathrm{k}, \mathrm{k}=\mathrm{l}=10 \mathrm{k} \). (20 marks) 1. Write down the equations of motion for this system. 2. Get the natural frequency of the system. 3. Get the mode shapes of the system. 4. If initial displacement of \( \mathrm{m}_{1} \) and \( \mathrm{m}_{2} \) is 0 and 5 , respectively, and initial velocity are zeros, get the free vibration response of the syatem.