the differential equation that describes the motion.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Consider a vertical spring-mass system. A long spring with spring constant k = 8 g/s² has a mass attached that
stretches the spring 245 cm. The damping coefficient is d = 8 g/s. At time t = 0, the mass is at the equilibrium
position (stretched due to gravity) and has a velocity of 3 cm/s downward.
Use a vertical coordinate system where x = 0 is the equilibrium length of the spring stretched due to gravity. Let
x be positive downwards (corresponding to stretching the spring).
Set up the differential equation that describes the motion. Solve the differential equation. State whether the
motion of the spring-mass system is harmonic (with no damping), underdamped, critically damped, or
overdamped. If the motion is harmonic or an underdamped oscillation, rewrite in amplitude-phase form.
Transcribed Image Text:Consider a vertical spring-mass system. A long spring with spring constant k = 8 g/s² has a mass attached that stretches the spring 245 cm. The damping coefficient is d = 8 g/s. At time t = 0, the mass is at the equilibrium position (stretched due to gravity) and has a velocity of 3 cm/s downward. Use a vertical coordinate system where x = 0 is the equilibrium length of the spring stretched due to gravity. Let x be positive downwards (corresponding to stretching the spring). Set up the differential equation that describes the motion. Solve the differential equation. State whether the motion of the spring-mass system is harmonic (with no damping), underdamped, critically damped, or overdamped. If the motion is harmonic or an underdamped oscillation, rewrite in amplitude-phase form.
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