HW1_assignment

HW1_assignment - 1 + z 2 and express the result in the form...

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SE 101C/ MAE 130C MECHANICS III: VIBRATIONS Dr. Van Den Einde Spring 2010 Page 1 HOMEWORK 1 Due: 4/14/10 1. A body weighing 25 lb is suspended from a spring of constant k = 160 lb/ft (see Figure 1). At time t = 0, it has a downward velocity of 2 ft/sec as it passes through the position of static equilibrium. Determine: a. The static spring deflection δ st b. The natural frequency of the system in both rad/sec ( ω n ) and cycles/sec (f n ) c. The system period T d. The displacement x as a function of time, where x is measured from the position of static equilibrium e. The maximum velocity v max attained by the mass f. The maximum acceleration a max attained by the mass. 2. Rao 1.9 3. Derive the equivalent spring constant for the system in Figure 2. 4. Rao 1.35 5. Given two complex numbers z 1 = (2+2i) and z 2 = (4-3i) a. Add z
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Unformatted text preview: 1 + z 2 and express the result in the form Ae i . b. Subtract z 1- z 2 and express the result in the form Ae i . c. Find the product of z 1 x z 2 and express the result in the form Ae i . d. Find the quotient z 1 /z 2 and express the result in the form Ae i . 6. Determine the sum of two vectors 2e i /4 and 3e i /6 and find the angle between the resultant and the first vector. 7. Rao 2.29 (solve Rao 2.26 first to be used in Rao 2.29) Figure 1 Figure 2 W=25lb x SE 101C/ MAE 130C MECHANICS III: VIBRATIONS Dr. Van Den Einde Spring 2010 Page 2 8. Draw the free-body diagram and derive the equation of motion for the system in Figure 4 using Newtons second law and Conservation of Energy. 9. Rao 2.53 10. Rao 2.73 11. Rao 2.89 12. Rao 2.106 Figure 4...
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HW1_assignment - 1 + z 2 and express the result in the form...

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