dynamis free vibrations problems, Exercises of Dynamics

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Example (1)

Consider the disk of the figure connected to two springs.Derive EOM for small angle

θ^ ( t ). [Inman/1.82] θ ( t )

Example (2)

Calculate the natural circular frequency

ωof the systemn^

shown in the figure. The mass and friction of the pulleys arenegligible.[J.L. Meriam & L.G. Kraige 8/25]

Example (4)

Determine the value of the viscous damping coefficient c forwhich the system has a damping ratio of (a) 0.5 and (b) 1.5.[J.L. Meriam & L.G. Kraige 8/36]

Example (5)

The motor has a mass of 43 kg and a radius of gyration of 100mm about O-O. If the motor has the natural frequency of freeoscillation at a speed of 360 rev/min, determine the stiffness kof each of the four identical spring mounts.[J.L. Meriam & L.G. Kraige 8/87]

Example (7)

The cannon fires a 4.5-kg connonball with an absolute velocityof 250 m/s at 20º to the horizontal. The combined mass of thecannon and its cart is 750 kg. If the recoil mechanism consistsof the spring of constant k = 27 kN/m and the damper withviscous coefficient c = 9000 Ns/m, determine the maximumrecoil deflection x

of the cannon unit.max^ [J.L. Meriam & L.G. Kraige 8/41]

Example (8)

Shock absorbers are tested by applying a 450-N force to therear bumper and meas. a static deflection of 75 mm. Uponsudden release of the force, the bumper rises and then falls toa max. of 12 mm below the unloaded equilibrium position onthe first rebound. Treat the action as a one-dimensionalproblem with an equivalent mass of half the car mass. Finddamping ratio

ζ^ for the rear end and

c^ for each shock absorber.

[J.L. Meriam & L.G. Kraige 8/42]

m= 1600-kgtruck^