Three springs and a mass are attached to a rigid, weightless bar PQ as shown in Fig. below Find the natural frequency of vibration of the system.

Calculate the equivalent spring equation and linear spring. Theory of vibration

A factory machine with a mass of 320 kg vibrations up and down with frequency of 8 Hz. Amplitude of engine movement of 2 mm. Calculate the maximum acceleration of the machine, and what is the maximum Newtonian force obtained?

A rigid block of mass ? is mounted on four elastic supports, as shown in the figure. A mass ? drops from a height ? and adheres to the rigid block without rebounding. If the spring constant of each elastic support is ?, derive the equation of motion and find the natural frequency of vibration of the system (a) without the mass ?, and (b) with the mass ?. Also, find the resulting motion of the system in case (b). By using lagrange energy method