4. A 1-kilogram mass is attached to a spring whose constant is 25 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 6 times the instantaneous velocity. (a) Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 15 m/s. Express the trigonometric portion of your answer in the form of one sine function containing a phase angle o (rounded-off to 4 decimal places). (b) Find the second time at which the mass passes through the equilibrium position heading upward. Round-off your answer to 2 decimal places.
4. A 1-kilogram mass is attached to a spring whose constant is 25 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 6 times the instantaneous velocity. (a) Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 15 m/s. Express the trigonometric portion of your answer in the form of one sine function containing a phase angle o (rounded-off to 4 decimal places). (b) Find the second time at which the mass passes through the equilibrium position heading upward. Round-off your answer to 2 decimal places.
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:4. A 1-kilogram mass is attached to a spring whose constant is 25 N/m, and the entire system is then submerged in a
liquid that imparts a damping force numerically equal to 6 times the instantaneous velocity.
(a) Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position
with an upward velocity of 15 m/s. Express the trigonometric portion of your answer in the form of one sine function
containing a phase angle o (rounded-off to 4 decimal places).
(b) Find the second time at which the mass passes through the equilibrium position heading upward. Round-off your
answer to 2 decimal places.
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