1) A weight of 18 lbs adheres to a spring and stretches it 4 inches. Find the motion equation if the weight is thrown from the balance position with a downward-directed speed of 2 ft/sec. Find the time when the weight first passes through the equilibrium point upwards.

2) A weight of 24 pounds is attached to a spring whose constant is 5 lb/ft. If the weight is released from a point 3 feet below the balance point in a medium that offers a resistance numerically equal to 3 times the instantaneous speed. Answer the following:

a) What kind of cushioning do we have in this case?

b) Find the motion equation

c) At what point is the weight when t is 1 sec?

3) A mass of 4 kg attached to a spring whose constant is 20 N/m is in a equilibrium position. Starting with t = 0, an external force: f(t) = e^t sin t , is applied to the system. Find the motion equation if the mass moves in a medium that gives you a resistance numerically equal to 8 times the instantaneous velocity. Plot the graph of the motion equation in the range t∈[0 ,10].

4) An L-R-C series circuit contains L = 1/2 H (Henry), R = 4.5 Ω, C = 1/10 F (farad) and E(t) = 110 volts. Determine the instantaneous load, q(t), on the capacitor if q(0)=1 and q'(0) = 0. What's the load after a long time?

5) The torsional movement of a suspended weight at the end of an elastic axis is governed by the differential equation IӨ'' + cӨ' + kӨ' = T(t), where “I” is the moment of inertia, “c” cushioning, “k” the elastic constant of the shaft and T(t) the applied torque. Find Ө (t) if after rest, a torsional force Tt=e-2t is applied to a system where I=1/4, c = 1, k = 4.

1. What is the UCL for the XBar chart based on the data below, with n=4, and ten set of samples for the weight of soft drinks are given. USL for the product is 355 g and LSL is 345. Daily production is 15000 units.

The UCL for the X-bar chart will be (circle the right answer).

a. 350.25

b. 345.92

c. 352.63

d. 349.27

2. What is the LCL for the Xbar chart for the problem with data given in question 1?

a. 352.63

b. 345.92

c. 349.27

d. 10.49

3. What is the UCL for the R-chart based on the data given in Problem 1?

a. 0

b. 4.6

c. 352.63

d. 10.50

4. What is LCL for the Rchart, based on the data given in problem?

a. -3.29

b. 0

c. 10.50

d. 4.6

In exercises 1–4, verify that the given formula is a solution to the initial value problem.

2. Powers of t.

b) y ′ = t^3 , y(0) = 5: y(t) = (1/5)t^(4) + 5

3. Sines and cosines.

a) x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) = sint

Find a subgroup G in symmetric (permutation) group Sn such that

(1) n = 4 and G is abelian noncyclic group

(2) n = 8 and G is dihedral group.

1. Assume the following for a project under evaluation:

** The project's life is 4 years.

** The total time zero, initial cost of $55,000.

** The total net operating cash flow each year is $15,000.

** In addition to the terminal year operating cash flow, there is a non-operating, terminal year cash flow of $8,000.

What is the project's IRR? Accept or reject the project? Again, assume the cost of capital for a project of this risk is 7%.

2. Barmin's Corp. has acquired an additional company by purchasing its outstanding stock. Analysts forecast a period of 2 years of extraordinary growth (20 percent), followed by 1 year of unusual growth (10 percent), and finally a normal (sustainable) growth rate of 6.5 percent annually indefinitely. The last dividend was D0= $1.00 per share and the required return is 8.6%. What is D4 (i.e., the dividend expected at end of period 4)?

1. Explain how an understanding of the 4 classes of materials and their general properties aid in the initial selection or elimination of materials suitable for a specific application. I.E. First outline some of the main general properties of each class, DO NOT GIVE EXAMPLES OF COMPONENTS AFTER EACH CLASS SECTION! Then describe how you would apply that knowledge to choose a suitable material for ONE specific component. ONLY ONE COMPONENT SHOULD BE PRESENTED AFTER YOU HAVE OUTLINED THE GENERAL PROPERTIES. I.E, SAY WHY ONE CLASS COULD NOT BE USED AND WHY ANOTHER CLASS CAN BE USED.

Exp 4 - Isolation of Eugenol

1) Draw the structure of eugenol and limonene. Identify the noteworthy functional groups in both structures.

(2) Search the internet and find an NMR spectrum for either eugenol or limonene (the one you isolated) and assign each of the peaks to the respective structure.

(3) What is the boiling point of eugenol and limonene? Could they be isolated from eachother? How?

4. A wagon of mass 14 tonnes is hauled up an incline of 1 in 20 by a rope which is parallel to the incline and is being wound round a drum of 1 m diameter. The drum, in turn, is driven through a 40 to 1 reduction gear by an electric motor. The frictional resistance to the movement of the wagon is 1.2 kN, and the efficiency of the gear drive is 85 per cent. The bearing friction at the drum and motor shafts may be neglected. The rotating parts of the drum have a mass of 1.25 tonnes with a radius of gyration of 450 mm and the rotating parts on the armature shaft have a mass of 110 kg with a radius of gyration of 125 mm.
At a certain instant the wagon is moving up the slope with a velocity of 1.8 m/s and an acceleration of 0.1 m/s2. Find the torque on the motor shaft and the power being developed. [T= 154 Nm, P=22,24 kW]

4. Suppose that 195 of the 738 observations in group 1 have a characterisitic of interest. And, suppose that 261 of the 815 observations in group 2 have this characterisitic.

(a) What is the sample proportion for group 1? (round to 5 digits after the decimal place)

(b) What is the sample proportion for group 2? (round to 5 digits after the decimal place)

(c) What is the difference in the sample proportions between groups 1 and 2? (round to 5 digits after the decimal place)

(d) What is the standard error for the difference in the sample proportions? (Use σp1−p2 and round to 5 digits after the decimal place.)

(e) What is the estimate of the left end of a 95% confidence interval? (Round to 5 digits after the decimal place.)

(f) What is the estimate of the right end of a 95% confidence interval? (Round to 5 digits after the decimal place.)

(g) Do we reject or not reject the null hypothesis that the population proportions are the same at the .05 level of significance? Reject Not reject