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3. A big slug weighing 10 pounds stretches a spring 1/4 foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance that is approximately equal to the velocity of the object) and then released from a position of 1/3 foot above the equilibrium with an downward velocity of 5/4 feet per second. (a) Set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all values to 2 decimal places for simplicity. (b) Graph your equation from (a), labeling the axes, and use your graph to find the second time where the slug is heading downwards and passes equillibrium. Write a sentence to summarize.

3. A big slug weighing 10 pounds stretches a spring 1/4 foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance that is approximately equal to the velocity of the object) and then released from a position of 1/3 foot above the equilibrium with an downward velocity of 5/4 feet per second. (a) Set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all values to 2 decimal places for simplicity. (b) Graph your equation from (a), labeling the axes, and use your graph to find the second time where the slug is heading downwards and passes equillibrium. Write a sentence to summarize.

Advanced Engineering Mathematics
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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**Problem 3: Spring-Mass System Analysis** A big slug weighing 10 pounds stretches a spring \( \frac{1}{4} \) foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance approximately equal to the velocity of the object) and then released from a position of \( \frac{1}{3} \) foot above the equilibrium with a downward velocity of \( \frac{5}{4} \) feet per second. (a) **Develop the Differential Equation (DE):** - Set up the differential equation representing this situation. - Show all steps to find the position equation for the spring. - Use \( x \) for the position and \( t \) for the time. - Round all values to two decimal places for simplicity. (b) **Graphing and Analysis:** - Graph the equation from part (a). - Label the axes on the graph. - Use the graph to determine the second time when the slug is moving downward and passes the equilibrium point. - Write a summary sentence. **Note:** Ensure clarity of mathematical notation and provide explanations alongside calculations for educational purposes.
Transcribed Image Text:**Problem 3: Spring-Mass System Analysis** A big slug weighing 10 pounds stretches a spring \( \frac{1}{4} \) foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance approximately equal to the velocity of the object) and then released from a position of \( \frac{1}{3} \) foot above the equilibrium with a downward velocity of \( \frac{5}{4} \) feet per second. (a) **Develop the Differential Equation (DE):** - Set up the differential equation representing this situation. - Show all steps to find the position equation for the spring. - Use \( x \) for the position and \( t \) for the time. - Round all values to two decimal places for simplicity. (b) **Graphing and Analysis:** - Graph the equation from part (a). - Label the axes on the graph. - Use the graph to determine the second time when the slug is moving downward and passes the equilibrium point. - Write a summary sentence. **Note:** Ensure clarity of mathematical notation and provide explanations alongside calculations for educational purposes.
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