1. A pebble stuck in a car tire tread will move up and down sinusoidally as the car drives, with a period equal to the circumference of the wheel. The document provides equations to calculate the pebble's position after given distances. 2. Water depth measurements at a dock vary sinusoidally with tides over a day. An equation is fitted to the data to determine depth at any time of day. 3. An equation models how water depth in a harbor will vary sinusoidally over time due to tides on a specific date, allowing calculations like minimum depth, time between high tides, and safe times for boat operation.