A rigid block of mass M is mounted on four elastic supports and the spring constant of each is k, as shown in the figure below. A small mass m drops from a height L and adheres to the rigid block without rebounding. (a) find the natural frequency of the system vibration without the mass m, and (b) with the mass m. (c) plot the response x(t) of the resulting motion of the system in part (a) for the time range (0 to 3 sec) or more. Take M= 200 kg, each k= 5 kN/m, and m=1 kg. The solution can be written in the form x(t) = A1 sin(wn. t) + A2 cos(wn. t) To calculate the response constants A1 =(vo/ wn), and A2=xo, where the initial conditions: xo= (100 * M /4 k), and vo= 10 m/s k m k M 0000 k