A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion. x(t) = 3 sin (2t) x m
A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion. x(t) = 3 sin (2t) x m
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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![**Spring-Mass System Problem**
A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
**Equation of Motion:**
\[ x(t) = 3 \sin(2t) \, \text{m} \]
This equation describes the displacement \( x(t) \) of the mass from its equilibrium position over time \( t \). The function \( 3 \sin(2t) \) indicates a sinusoidal motion, with an amplitude of 3 meters and a frequency that corresponds to a period of \( \pi \) seconds. The spring exhibits harmonic motion with these parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba28fbe0-fc04-46bc-bd01-9a9731588fb8%2F2175d139-09f1-4f40-a418-ddf55f2f4c84%2F1w576s_processed.png&w=3840&q=75)
Transcribed Image Text:**Spring-Mass System Problem**
A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
**Equation of Motion:**
\[ x(t) = 3 \sin(2t) \, \text{m} \]
This equation describes the displacement \( x(t) \) of the mass from its equilibrium position over time \( t \). The function \( 3 \sin(2t) \) indicates a sinusoidal motion, with an amplitude of 3 meters and a frequency that corresponds to a period of \( \pi \) seconds. The spring exhibits harmonic motion with these parameters.
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