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

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.15P

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