A mass weighing 6lb stretches a spring 5 in. If the mass is pushod upward, contracting the spring a distance of 7 in and then set in motion with a downward velocity of 5 ft/s, and if there is no damping and no other external force on the system, find the position u of the mass at any time t. Determine the frequency (w), period (T), amplitude (R), and phase (6) of the motion. NOTE: Enter ezact answers. Use t as the independent variable.
A mass weighing 6lb stretches a spring 5 in. If the mass is pushod upward, contracting the spring a distance of 7 in and then set in motion with a downward velocity of 5 ft/s, and if there is no damping and no other external force on the system, find the position u of the mass at any time t. Determine the frequency (w), period (T), amplitude (R), and phase (6) of the motion. NOTE: Enter ezact answers. Use t as the independent variable.
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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![A mass weighing 6 lb stretches a spring 5 in. If the mass is pushed upward, contracting the spring a distance of 7 in and then set in motion with a downward velocity of 5 ft/s, and if there is no damping and no other external force on the system, find the position \( u \) of the mass at any time \( t \). Determine the frequency (\(\omega_0\)), period (\(T\)), amplitude (\(R\)), and phase (\(\delta\)) of the motion.
**NOTE:** Enter exact answers. Use \( t \) as the independent variable.
\[ u(t) = \]
\[ \omega_0 = \text{ rad/s} \]
\[ T = \text{ s} \]
\[ R = \text{ ft} \]
\[ \delta = \text{ rad} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52cb9bca-e676-4732-b7fa-23209512b0cf%2Fb20110de-bc2c-46c1-9000-d9a512ff1e14%2F29x8po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A mass weighing 6 lb stretches a spring 5 in. If the mass is pushed upward, contracting the spring a distance of 7 in and then set in motion with a downward velocity of 5 ft/s, and if there is no damping and no other external force on the system, find the position \( u \) of the mass at any time \( t \). Determine the frequency (\(\omega_0\)), period (\(T\)), amplitude (\(R\)), and phase (\(\delta\)) of the motion.
**NOTE:** Enter exact answers. Use \( t \) as the independent variable.
\[ u(t) = \]
\[ \omega_0 = \text{ rad/s} \]
\[ T = \text{ s} \]
\[ R = \text{ ft} \]
\[ \delta = \text{ rad} \]
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