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Suppose that car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g=32 ft/sec². T= 0.436 ✔seconds. 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions ? y(0) = -0.436 X ft. and y'(0) = ft/sec. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -6.93 lb-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)=0 ft and y(0)=-10 ft/sec. y(t) =

Suppose that car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g=32 ft/sec². T= 0.436 ✔seconds. 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions ? y(0) = -0.436 X ft. and y'(0) = ft/sec. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -6.93 lb-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)=0 ft and y(0)=-10 ft/sec. y(t) =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.4: Applications
Problem 9EQ
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1. Suppose that a car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g=32 ft/sec². T= 0.436 seconds. 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions ? y(0) = -0.436 X ft. and y'(0) = ft/sec. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -6.93 lb-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)=0 ft and y(0)=-10 ft/sec. y(t) =
Transcribed Image Text:1. Suppose that a car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g=32 ft/sec². T= 0.436 seconds. 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions ? y(0) = -0.436 X ft. and y'(0) = ft/sec. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -6.93 lb-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)=0 ft and y(0)=-10 ft/sec. y(t) =
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