A mechanical system is depicted in the figure below. A pinion with fixed rotation axis passing through C2 meshes with a translatory rack of mass m = 0.8 kg. The rack, which is supported on two identical guides (bearings), each of damping coefficient c = 12 N s/m, meshes with another solid pinion that, as a result, rolls without slippage on another fixed rack. Derive the differential equation describing the movement of the system. Determine transfer function G(s) = X(s)/F(s) where X(s) is the Laplace transform of x(t) and F(s) is the Laplace transform of f (t). Find x(t) if the input is f(t) = 80(t) = step function. The system parameters are: J1 = 0.001 kg m² and J2 = 0.0003 kg m², m̟ = 0.4 kg, the radii R1 = 0.05 m, R2 = 0.07 m, R = 0.06 m, the stiffness k = 160 N/m, %3D a. b. C. Pinion R Rack Guide A R1 Pinion R2 Fixed rack

A mechanical system is depicted in the figure below. A pinion with fixed rotation axis passing through C2 meshes with a translatory rack of mass m = 0.8 kg. The rack, which is supported on two identical guides (bearings), each of damping coefficient c = 12 N s/m, meshes with another solid pinion that, as a result, rolls without slippage on another fixed rack. Derive the differential equation describing the movement of the system. Determine transfer function G(s) = X(s)/F(s) where X(s) is the Laplace transform of x(t) and F(s) is the Laplace transform of f (t). Find x(t) if the input is f(t) = 80(t) = step function. The system parameters are: J1 = 0.001 kg m² and J2 = 0.0003 kg m², m̟ = 0.4 kg, the radii R1 = 0.05 m, R2 = 0.07 m, R = 0.06 m, the stiffness k = 160 N/m, %3D a. b. C. Pinion R Rack Guide A R1 Pinion R2 Fixed rack

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

A mechanical system is depicted in the figure below. A pinion with fixed rotation axis
passing through C2 meshes with a translatory rack of mass m = 0.8 kg. The rack, which is
supported on two identical guides (bearings), each of damping coefficient c = 12 N s/m, meshes
with another solid pinion that, as a result, rolls without slippage on another fixed rack.
Derive the differential equation describing the movement of the system.
Determine transfer function G(s) = X(s)/F(s) where X(s) is the Laplace
transform of x(t) and F(s) is the Laplace transform of f(t).
Find x(t) if the input is f(t) = 80(t) = step function. The system parameters
are: J1 = 0.001 kg m² and J2 = 0.0003 kg m², m. = 0.4 kg, the radii R1 = 0.05 m, R2 = 0.07
m, R = 0.06 m, the stiffness k = 160 N/m,
%3D
a.
b.
C.
Pinion
J2
R
Rack
Guide
RI
Pinion
R2
Fixed rack

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