6. A machine of mass m = 2kg is supported by four springs and a damper of coefficient of damping c = 1 N.s/m, as shown in Figure 6. It is observed that the equilibrium position is established after the springs have depressed by 24.5 mm under the weight of the machine. At time t=0, the machine is pushed down from its equilibrium position by y = 100mm, as shown, and then released. (a) For the system, () Calculate the total stiffness, kr, of the four springs and the natural circular frequency of vibration, o,, (H) The damping ratio, 5. and hence identify the prevaling type of Damping. (b) For the ensuing vibration of the machine, () Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations.

answer ASAP would be appreciated

The maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil velocity is to be between 8 m/s and 10 m/s, find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least 500 kg.