# Project #43686 - Harmonic Oscillations (Motion on the circle)

This is a project for a Master student, so please, you must have a FULL background and knowledge on every single question. I want a full detailed and explained answers (as I well represent the answers my self). also to provide an extra excel document for some of the questions.

Thank you.

The homework:

Hand in one word document with your answers. You can make plots by hand or by excel, and copy-paste the results in the word document. Always explain briefly how you found the answer. Dont forget your units! Any information missing in the question you are free to fill in yourself.

A turtle and a hare are running on two different circles. The hare runs on a circle with radius 400m, at a velocity of 20km/hr and initial phase of 0 degrees. The turtle runs on a circle with radius 1m at a velocity of 50cm/min and has a head start with an initial phase of 90 degrees.

Question 1: What is the angular frequency, frequency and period of turtle and hare. Question 2: Consider a time point 10 minutes after the start of the race.

1. a)  What is the phase of hare and turtle?

2. b)  What is the X- and Y-coordinate of the hare and turtles position?

3. c)  How far apart are they?

Question 3: Consider the first hour after the start of the race.

1. a)  Plot the phase of hare and turtle as a function of time.

2. b)  Plot the X- and Y-coordinate of the hare and turtle as a function of time.

3. c)  Plot the distance between them as a function of time.

4. d)  When is the first time that they are in-phase and opposed-phase?

5. e)  How often does it happen that they are in-phase?

 Subject Mathematics Due By (Pacific Time) 10/17/2014 07:00 am
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