One of the largest sewing machines in the world has a flywheel (which turns as the machine sews) that is 5 feet in diameter. The highest point of the handle at the edge of theflywheel is 9 feet above the ground, and the lowest point is 4 feet. The wheel makes a complete turn every 2 seconds. Write a function h (in feet) of the handle as a function oftime t (in seconds, given that the handle is at its lowest point when t=0.)f(x)= type your answer.

Answered: Une of the largest sewing machines in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

One of the largest sewing machines in the world has a flywheel (which turns as the machine sews) that is 5 feet in diameter. The highest point of the handle at the edge of the
flywheel is 9 feet above the ground, and the lowest point is 4 feet. The wheel makes a complete turn every 2 seconds. Write a function h (in feet) of the handle as a function of
time t (in seconds, given that the handle is at its lowest point when t=0.)
f(x)= type your answer.

Expert Solution

Step 1

The motion of a wheel is very significant in trigonometry. It is a periodic motion. Therefore, the motion can be defined in the form of a sinusoidal function. The function may be either sine function or cosine function. The representation consists of a vertical shift, horizontal shift, period. The vertical shift is the average of the maximum and minimum height. The amplitude is the half of the difference of the maximum and minimum height. When the graph is a reflection, the amplitude becomes negative.