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#4) A mass weighing 4 pounds is attached to a spring whose constant is 2 lbs/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 8 feet/second. a) Determine the function modeling the motion of the mass at time t. b) Determine the time at which the mass passes through the equilibrium position. c) Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant? #5) (20 points) (20 points) A tank contains 200 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gallons per minute. a) If the well-mixed solution is pumped out at a rate of 4 gallons per minute, find the number A(t) of pounds of salt in the tank at time t. b) If the well-mixed solution is pumped out at the rate of 3 gallons per minute, find the number A(t) of pounds of salt in the tank at time t.

#4) A mass weighing 4 pounds is attached to a spring whose constant is 2 lbs/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 8 feet/second. a) Determine the function modeling the motion of the mass at time t. b) Determine the time at which the mass passes through the equilibrium position. c) Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant? #5) (20 points) (20 points) A tank contains 200 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gallons per minute. a) If the well-mixed solution is pumped out at a rate of 4 gallons per minute, find the number A(t) of pounds of salt in the tank at time t. b) If the well-mixed solution is pumped out at the rate of 3 gallons per minute, find the number A(t) of pounds of salt in the tank at time t.

Advanced Engineering Mathematics
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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#4) A mass weighing 4 pounds is attached to a spring whose constant is 2 lbs/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 8 feet/second. a) Determine the function modeling the motion of the mass at time t. b) Determine the time at which the mass passes through the equilibrium position. c) Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant? #5) (20 points) (20 points) A tank contains 200 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gallons per minute. a) If the well-mixed solution is pumped out at a rate of 4 gallons per minute, find the number A(t) of pounds of salt in the tank at time t. b) If the well-mixed solution is pumped out at the rate of 3 gallons per minute, find the number A(t) of pounds of salt in the tank at time t.
Transcribed Image Text:#4) A mass weighing 4 pounds is attached to a spring whose constant is 2 lbs/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 8 feet/second. a) Determine the function modeling the motion of the mass at time t. b) Determine the time at which the mass passes through the equilibrium position. c) Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant? #5) (20 points) (20 points) A tank contains 200 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gallons per minute. a) If the well-mixed solution is pumped out at a rate of 4 gallons per minute, find the number A(t) of pounds of salt in the tank at time t. b) If the well-mixed solution is pumped out at the rate of 3 gallons per minute, find the number A(t) of pounds of salt in the tank at time t.
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