ME 143 1st Long Exam 2SY 2014-2015 March 17, 2015

1. For the oscillation of the spring and mass system, m = 1 kg. Determinea. damped natural frequencyb. damping ratioc. critical damping coefficientd. damping constante. spring constantf. natural frequency of the systemg. initial conditions h.i. the equation of motion of the systemj. forcing function

2. Referring to the figure below, draw the displacement function for a forced damped spring and mass system having a damping ratio of 0.3 and having a forcing function with a frequency ratio of 1.4, mass m = 1 kg, spring constant k = 5,000 N/m and forcing function amplitude is 500 N.

3. Develop the differential form of Newton’s equation of motion for the spring mass system indicated on the right. The mass meq displacement is y1 and the wheel, which follows the road profile has a sinusoidal shape with maximum displacement Y2. At what speed will the vibration amplify?

4. An electric motor weighing 4,000 N and running at 1,800 rpm is supported on four springs with a stiffness of 10,000 N/m. The rotor has a weight of 500 N with its center of mass located at a distance of 0.000254 m from the axis of rotation. Determine:a. The speed at which resonance will occur.b. The amplitude of the steady state displacement of the motorc. If the motor speed is increased by 20%, how will the amplitude of the steady state

displacement change?d. How would the system amplitude be affected by the rotational speed of the motor? Use diagrams to augment

your explanation.

5. Derive the equation of motion for the system shown. Determine the damped and undamped natural frequency and the damping ratio.