A block of mass m, resting on a frictionless horizontal plane is connected through a spring of constant k to a homogenous uniform rod of mass M and length L, as shown in Figure 5. Given that L = 0.4 m, M = 2.69 kg, m = 15.602 kg, k = 100 N/m, calculate the followings: a. The natural frequencies (Answer: 6.91 rad/s ; 40.65 rad/s) b. The ratio of amplitudes c. Draw the shapes of normal modes (Answer: 1/0.87 ; 1/-3.44)