A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s² for the acceleration due to gravity.) 12 Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. 3 What is the position (in ft) of the mass at this instant? ft
A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s² for the acceleration due to gravity.) 12 Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. 3 What is the position (in ft) of the mass at this instant? ft
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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Transcribed Image Text:A mass weighing 4 pounds is attached to a spring with a spring constant of 2 lb/ft. The medium applies a damping force equal to the instantaneous velocity. Initially, the mass is released from 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in seconds) at which the mass passes through the equilibrium position. (Use \( g = 32 \, \text{ft/s}^2 \) for gravitational acceleration.)
Time: \( \frac{1}{12} \, \text{s} \)
Find the time (in seconds) after the mass passes through the equilibrium position when it attains its maximum displacement from the equilibrium position.
Time: \( \frac{1}{3} \, \text{s} \)
What is the position (in feet) of the mass at this instant?
Position: ___ ft
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