The figure shows a structure composed of a beam and a system of springs that supports a box weighing 20 kips. Use the spring stiffness and mechanical properties of the beam given in the figure. Using the vertical displacement of the box as the degree of freedom and the equivalent spring method, determine the equation of motion for free vibrations. Also calculate the frequency and natural period. You can neglect the self-weight of the beam.

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A pendulum is made up of a spring with a mass attached to the end. The spring is arranged to lie in a straight line, by wrapping the spring around a massless bar. The equilibrium length of the bar is “l”. Using lagrange’s equations, find the equations of motion.

pls ans quickly take p= 2 q=0 r=1

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Machine Dynamics: In the mechanism in the figure; The 2nd limb in the horizontal position rotates with a constant angular velocity of 100 rad/s under the effect of external torque T12.Obtain the equations of change of axial internal force, shear force and bending moment in limb 3 due to inertia and bond forces at the specified position, ignoring frictions.(O2 joint point is the center of gravity of limb 2) "Detailed Solution Please"

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

I Review Use a block-and-spring model like that shown in the figure, but suspended from a vertical position and subjected to a periodic support displacement 8 = 8psinwnt, determine Express your answer as an equation in terms of some or all of the variables y, a (a = y), ki, m, wn (wn = V). wn, t, and on. the equation of motion for the system, and obtain its general solution. Assume positive displacement is downward. (Figure 1) Va AZo| t vec k la+ m k sin @, t m That's not quite right. Please check your formatting and try again. No credit lost. Try again. Submit Previous Answers Request Answer Part B Obtain the general solution of the above equation. Figure 1 of 1 Express your answer in terms of some or all of the variables A, B, t, k, m, wn (Wn = 1/), 80, and wo. V ΑΣφ vec Equilibrium position A sin (@,1) +B cos (@,1) sin (@,) mw,“ 1- k y = Bd8 = 8, sin d Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining

k 0.5m- 1m The moveable mass is removed, the spring stiffness increased to k= 500 N/m and a viscous damper is added to the system. The new system is show in the figure above. The mass of the slender rod remains 6 kg. For what value of the damping coefficient C will the system be critically damped? (round your answer to the nearest whole number) A Ns/m