2. A pendulum exhibits simple harmonic motion when it is released at an angle θ = 9°. The length of the pendulum is l=0.86 m, and the pendulum bob has a mass m=0.3 kg.

a. What is the pendulum’s frequency?

b. Use energy conservation to find the pendulum bob’s speed when it passes through the lowest point of the swing? Assume that the difference in height between the lowest part of the swing and the highest part of the swing is delta H= l(1-cos(θ))

c. What is the total energy of the system?

Assume that there was a starburst that produced 10¹¹ solar masses of stars with a minimum mass of 0.3 solar masses and a maximum mass of 100 solar masses. The number of stars as a function of mass is N(M) = KM^-2.35, where K is a normalization constant. The current turnoff mass of the population is 1 solar mass

1. Compute the number of stars and the total mass of stars that are still on the main sequence.
2. Assume that all stars with masses between 1 and 8 solar masses became white dwarfs. Compute the total number of white dwarfs in this population

Assume in a Bertrand model, there are 3 identical firms in the market with the same constant marginal cost of 30. The demand function is P = 150 ? Q. Firms share the monopoly profit equally if they participate in the cartel. With probability 0.3 the cartel is detected by the end of period t, in which case each cartel member has to pay the fine $1000. Cartel investigation takes one period. If detected by the end of period t, the cartel is disbanded at the end of the period and the firms return to the noncooperative game permanently. Derive the condition required for the cartel to succeed

12. If a Hall voltage of 2.50 x 10^-3V is produced by a 0.300-T field applied across a 1.50-cm-diameter aorta, what is the blood velocity inside?

14. A solenoid has 300 turns and a length of 10.0 cm. When a current of 2.50 A flows through the solenoid, how strong is the magnetic field produced inside it?

15. In a mirror's ray diagram, the distance between the object and the image is 30 cm. The magnification of the image is -0.3. What type of mirror is used and what is the focal length of the mirror?

A square conducting loop of side length a = 24 cm sits in three-dimensional space, such that its area vector points along the vector -i - 4j + k.

A uniform magnetic field of strength B = 0.04 mT points along the positive z-axis.

A current of I = 0.3 mA is run through the loop. Find the net force on the loop.

Find the torque on the loop. (Note it should be of the form (Tx , Ty , Tz) with appropriate numbers)

What is the magnetic dipole moment of the current loop?

The monthly ambulatory visit shown in the Table below occurred in an outpatient clinic.

1. Prepare a forecast for January visits, using the simple exponential smoothing method with α = 0.3.
2. If α = 0.5, what is the predicted value for January visits?
3. If α = 0.0, what is the predicted value for January visits
4. If α = 1.0, what is the predicted value for January visits
5. Which alpha produces the best forecast?

The reliability of a particular skin test for tuberculosis (TB) is as follows: the sensitivity of the test is 0.9 (the test comes back positive 90% of the time if the subject has TB) and the specificity of the test is 0.95 (if the subject does not have TB, the test comes back negative 95% of the time). In a large population, only 0.3% (0.003) of the people have TB. A person is selected at random and given the test, which comes back positive.

a) create a hypothetical 100,000 table to answer question b.

b) What is the probability that that person actually has TB?

You are analysing four different stocks. The expected market return is 10% with a standard deviation of 20%. The risk free-rate is 2%. Assume the Capital Asset Pricing Model (CAPM) holds and you base your conclusion completely on CAPM. Indicate in the table below which of the following securities is underpriced, overpriced or correctly priced.

A Unity feedback system has an open loop transfer function of

G(s) = K / s (s+1) (s+5)

Draw the root locus plot and determine the value of K to give a damping ratio of 0.3 A network having a transfer function of 10(1 +10s) /(1 +100s) is now introduced in tandem. Find the new value of K, which gives the same damping ratio for the closed -loop response. Compare the velocity error constant and settling time of the original and the compensated systems