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"anslated by Google m-5 kg m k-10 kN/m c-200 N.s/m In the system shown in the static equilibrium position, the rod of mass m and the object of mass 2m are massless. It is connected to the reel by massless rigid rods as shown in the figure. According to this, a) Obtain the differential equation of the x(t) vibrations of the 2m mass object of the system Determine its natural frequency and damping ratio. b) After 3 periods, the X vibration amplitude of the free vibrations of the system decreases by 60% What should be the damping coefficient in the system? Calculate. c) in a situation where the system leaves the equilibrium position, obtain the value that the c coefficient of the system should take in order for the system to return to the equilibrium position as quickly as possible. d) Neglecting the damping in the system, what will be the acceleration of the rod when it is at x-5 cm, calculate. e) x(0)-0.05 m, x(0)=0.03 m/slution x(1) corresponding to the initial conditions and plot the xit-t graph for at least 3 periods. k-1000 N/m c-50 Ns/m m-8 kg y(t) [cm] M t [san] 10 15 20 y(t) = *! (1 − . In the mass-spring-damper system in the figure, the platform to which the spring and damper elements are attached T-6 second period with Yg-5 cm x(0)=47/(1-7) is making the move. Mass 1 Find the x(1) time solution of the motion. NOTE: Express what you did in your homework step by step and in an orderly manner. You have to submit the printout of the program you use for graphic drawing, the numerical values you find and the graphics MAK 315-MECHANICAL VIBRATIONS HOMEWORK 1 Deadline: 09.05.2022 Kütlesiz makara 1/2 1/2 5666666 www