For a certain mass-spring system m = 100 kg and k = 8000 N/m. Determine the value of the critical damping constant C_c and the damped natural frequency W_d and the logarithmic decrement d if C = C_c/3

Mechanical Vibrations Question is image

Question 2: a. Determine the differential equation of motion and find the natural frequency (w). Also establish the critical damping for the system shown in Fig. 2a b. If the system has a mass of 0.907 kg with spring stiffness of 7.0 N/cm. Determine the critical damping coefficient.

A mass of 5kg on a spring with k=5N/m and damping constantly=6Ns/m. Using forcing function cos(ωt), find the value of ω that causes practical resonance.

The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…

Consider the following system. Assumem = 4kg,k = 2000 N/m and c = 20N.s/m. The damping ratio of the first mode is: m Xj k m X2

Determine the damping factor and natural frequency for the second-order system below and determine the type of response. ωn=  ζ =  system type =

Vibrations Engineering:  Mass = 10 kilogramsSpring constant = 400 Newtons per meterPeriodic Force = 6 KilonewtonsForcing Frequency = 5 radians per secondDamping coefficient = 200 Newton second per meter Calculate: (Express the final answer in 4 significant digits) -the critical damping in Newton second per meter -the damping factor

Pravinbhai

Figure below shows a single degree of freedom system. The system has a moment of inertia I =37 kg.m² about point O, the stiffness and damping values are k =548 N/m and C =113 N.s/m, respectively. Considering a =1.6 m and b =0.7 m, find the damped natural frequency of the system in rad/s. a b C www