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Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. Consider a simple wheelchair with a suspension system (bumper) composed of a spring and a dashpot as illustrated in the figure. It is desired that as the patient sits on to the chair resulting in the system settling at a new equilibrium 5 cm lower than the initial position as quickly as possible without overshooting this equilibrium (critically Fe(t) damped system). • Fe(t) is the gravitational force exerted by the patient, weight of the patient is 100 kg. (The acceleration due x(t) K. to gravity, g = 9.8 m/s²) "m" is mass of the wheelchair, 50 kg "B" is the damping coefficient of the dashpot, N/(m/s) 777 "K." is the stiffness (inverse of compliance) of the spring, N/m "x" is the change in position of the seat with respect to ground. 1 Inverse Laplace transform of u(t) A; e-atu(t) §. ;te-at, "u(t) sta (sta)? a. Drive the differential equation that relates x(t) to Felt) b. Determine the transfer function between x(t) and Fe(t) and express it in standard form. c. Find the spring constant K,. d. Find the damping coefficient B of the dashpot. e. Express the change in the position of the chair (x) as a function of time in terms of the system parameters.
Transcribed Image Text:2. Consider a simple wheelchair with a suspension system (bumper) composed of a spring and a dashpot as illustrated in the figure. It is desired that as the patient sits on to the chair resulting in the system settling at a new equilibrium 5 cm lower than the initial position as quickly as possible without overshooting this equilibrium (critically Fe(t) damped system). • Fe(t) is the gravitational force exerted by the patient, weight of the patient is 100 kg. (The acceleration due x(t) K. to gravity, g = 9.8 m/s²) "m" is mass of the wheelchair, 50 kg "B" is the damping coefficient of the dashpot, N/(m/s) 777 "K." is the stiffness (inverse of compliance) of the spring, N/m "x" is the change in position of the seat with respect to ground. 1 Inverse Laplace transform of u(t) A; e-atu(t) §. ;te-at, "u(t) sta (sta)? a. Drive the differential equation that relates x(t) to Felt) b. Determine the transfer function between x(t) and Fe(t) and express it in standard form. c. Find the spring constant K,. d. Find the damping coefficient B of the dashpot. e. Express the change in the position of the chair (x) as a function of time in terms of the system parameters.
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