Consider the following mechanical system consisting of a massless rod of length L connected to a ball of mass m. The system has a rotational damper b, a spring constant k, and is subject to gravitational acceleration g. The input into the system is a torque u(t). 10 L im k torque input u(t) Derive and fully simplify the transfer function: G(s) = gravity 'm Ⓒ(s) U(s) Make sure to expand/cancel terms such that the numerator and denominator are each a polyno- mial in terms of s (with coefficients in terms of the constants of the problem: k, m, b, L as needed). Use small angle approximations.

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
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Consider the following mechanical system consisting of a massless rod of length L connected to
a ball of mass m. The system has a rotational damper b, a spring constant k, and is subject to
gravitational acceleration g. The input into the system is a torque u(t).
4
torque input
u(t)
10 L
Lamb..
'm
k
Derive and fully simplify the transfer function:
gravity
(s)
U (s)
G(s)
Make sure to expand/cancel terms such that the numerator and denominator are each a polyno-
mial in terms of s (with coefficients in terms of the constants of the problem: k, m, b, L as needed).
Use small angle approximations.
Transcribed Image Text:Problem Consider the following mechanical system consisting of a massless rod of length L connected to a ball of mass m. The system has a rotational damper b, a spring constant k, and is subject to gravitational acceleration g. The input into the system is a torque u(t). 4 torque input u(t) 10 L Lamb.. 'm k Derive and fully simplify the transfer function: gravity (s) U (s) G(s) Make sure to expand/cancel terms such that the numerator and denominator are each a polyno- mial in terms of s (with coefficients in terms of the constants of the problem: k, m, b, L as needed). Use small angle approximations.
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