Derive the differential equation of motion for the system shown in its equilibrium position. Neglect the mass of link AB and assume small oscillations. Use the values m₁ = 22 kg, m₂ = 31 kg, k = 800 N/m, c = 163 N-s/m, a = 340 mm, and b = 610 mm and calculate the damping factor 3. m2 m B

+ b 3. A tuning fork is an example of a "resonant system", that is, one that has a low damping ratio. A model of a (half) tuning fork is rod of mass m with air drag modeled as a damper connected approximately at its middle, and a torsional spring at the base of the cantilever. Assume the cantilever rotates back and forth about its pivot by a small angle o. Because other forces are much larger, you can reasonably neglect the effect of gravity in this model. The moment of inertia of a cantilevered beam pinned at one end is equal to ml2, where I is its length. (a) What is the natural frequency of this system if m= 0.1 kg and k = 2548 Nm/rad, and 1 = 0.1 m. Please give the value in rad/s and Hz. (b) Find an upper bound on the damping coefficient b that insures that the damping ratio of the tuning fork is no greater than = 0.01. (c) For this damping ratio, what is the damped natural frequency of the system? (d) For this damping ratio, what is the decay rate (the size of the exponent…

find the equations of motion using the lagrange equations of motion. Point A and C are moving vertically, points D and B are moving horizontally. the unloaded spring has length equal to l*sqrt(2). Each rod has mass m amd length l, spring constant is equal to k

The system shown consists of a mass m and a massless rod oflength l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equationof motion assuming small oscillations. Determine the natural frequency of thesystem.

4.Find equation of motion and the period of the mass-spring systen k₂ = 2k, m Fig 1 k₁ =3k₁

Find the equations of motion for a lever of length 2a and of mass M rotating around its tip A 20

Find the motion equations of the system shown in the figure.

The uniform bar shown has mass m, length l, and mass momentof inertia I about its mass center. The bar is supported by two springs k1and k2, as shown in the figure. Obtain the differential equation of motion anddetermine the natural frequency of the system in the case of small oscillations. (USE VIRTUAL WORK METHOD)

For the system shown in the figure, set up the equation of motion for the mass, m, and solve for the steady state amplitude and phase angle.

For the system shown in figure below, derive the differential equation of motion for small oscillation. If m1=m2=1 kg, k1=k2=1000 N/m, c1=c2=10N·s/m, a=b=0.5 m, and l=1 m find the solution after 1 s provided that the initial angular displacement is zero and the initial angular velocity is 5 rad/s. Assume that the rod is massless.