S302, Kewley-Port 9/22/07

Homework 5
IMPEDANCE, EXPONANTS & LOGARITHMS

1. a) Write down the equation for calculating mass reactance, Xm .

b) Explain how Xm changes with frequency.

c) If frequency is high, how important is Xm in calculating total impedance?

d) If Xm = Xc for some system, and R = 2 ohms, explain the relation between the total impedance and the observed vibration of the system. Will the system be in natural vibration?

2. Consider the following parameters of a system. The resistance R=10 ohms, the mass reactance Xm= 22 ohms, and the compliant reactance Xc = 2 ohms. (a) Draw tttthe viector relationship with accurate lengths of the vectors that looks like Fig. DKP-1 in the handout. (b) Compute the magnitude of the impedance, Z.

3. Solve the following problems using the laws of exponents.

1. 22.5 · 20.5

2. 103 · 105 · 102

3. 24/22

4. 10-8/10-12

5. 5-8/5-8

6. (22)3

7. (105)0.5

8. (5 · 2)3

9. 53 · 23

4. Solve the following problems using the laws of logarithms

1. log10(3 · 2)

2. log10(5.32 · 100)

3. log10(3/2)

4. log10(5.32/100)

5. log10(32)

6. log10(10)2

7. log10(1/2)

8. log10(1/10)