CMSI 186 Problem Set #2

CMSI 186 Problem Set #2 Discrete Simulation Due Thursday, February 8

Overview

In this assignment you will program discrete simulations of a clock and a water tank to answer some questions about their behavior.

You will want to define a class of Clock objects, with methods like void tick() and int hour(). Click here to see a class summary for a fairly minimal version of public class Clock.

You must write unit tests for the class' methods before you begin coding the methods themselves.

Problem One

Make a program that determines all of the times during a twelve-hour day at which a clock's hands form a given angle. Your program should perform a discrete simulation of a clock, using the basic approach and program structures that were discussed in class.
Your program will be invoked like this:
```
    java ClockSolver x grain
```
where x indicates the sought-after angle (in degrees), and grain indicates the amount of time that will drive the simulation (in seconds). x must be a double in the range
```
      0.0 <= x < 360.0.
```
grain is optional; if specified, it must be a double in the range
```
      0.0 < grain <= 1800.0; 
```
if omitted, it should be set to one second.

You should test your program on all sorts of inputs. What happens as the grain gets very small (e.g., 0.0001)? Apart from the increased running time of the program, do you notice anything funny about the outputs? Give an explanation for this behavior.

Problem Two

A tank, which has a capacity of two hundred fifty gallons, is initially empty and is connected to three pipes, A, B, and C. Water flows into the tank through A and B, and out via C. Here are their flow rates, where amt(t) denotes the number of gallons of water in the tank at time t:

for 0 <= t < 5 minutes: amt(t) / 10 gallons per minute
for 5 <= t < 12 minutes: amt(t) / 8 gallons per minute
for 12 <= t minutes: switches every minute between amt(t) / 6 and amt(t) / 4 gallons per minute

for 0 <= t < 4 minutes: 4 gallons per minute
for 4 <= t < 11 minutes: 9 gallons per minute
for 11 <= t minutes: switches every 90 seconds between amt(t) / 7 and amt(t) / 5 gallons per minute

At what time, if ever, will the tank be filled to capacity? Your program should output system status reports after every minute of simulated time and, of course, at the conclusion of the simulation.

Return to: CMSI 186 home page
Revised: January 23, 2006