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 damped system). Fe(t) is the gravitational force exerted by the patient, weight of the patient is 100 kg. (The acceleration due 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) "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. Inverse Laplace transform of u(t); m -ite-atu(t) +₂ s+a Fe(t) -000 e-atu(t) • a. Drive the differential equation that relates x(t) to F.(t) b. Determine the transfer function between x(t) and Fe(t) and express it in standard form. c. Find the spring constant K₁. 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 x(t) (s+a)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 damped system). Fe(t) is the gravitational force exerted by the patient, weight of the patient is 100 kg. (The acceleration due 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) "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. Inverse Laplace transform of u(t); m -ite-atu(t) +₂ s+a Fe(t) -000 e-atu(t) • a. Drive the differential equation that relates x(t) to F.(t) b. Determine the transfer function between x(t) and Fe(t) and express it in standard form. c. Find the spring constant K₁. 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 x(t) (s+a)²

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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