Assignment:
Q1. Suppose Anytown, USA has a fixed population of 200,000. On March 1, 3000 people have the flu. On June 1, 6000 people have it. If the rate of increase of the number N(t) who have the flu is proportional to the number who don’t have it, how many will have the disease on September 1?
Q2. Suppose that a motorboat is moving at 30 ft/sec when its motor suddenly quits, and that 5 seconds later the boat has slowed to 15 ft/sec. Assume that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
Q3. A mass of 25g is attached to a vertical spring with spring constant k = 3 dyne/cm. The surrounding medium has a damping constant of 10 dyne*sec/cm. The mass is pushed 5 cm above its equilibrium position and released. Find (a) the position function of the mass, (b) the period of the vibration, and (c) the frequency of the vibration.
Provide complete and step by step solution for the question and show calculations and use formulas.