Question 5: Consider the mechanical system shown on the next page. Note that this figure contains geometric information. A uniform, homogeneous, slender rod with length L [m] and mass m [kg] can rotate about fixed point O. Its orientation is given by angle 8(t) [rad], which is defined positive in counterclockwise direction. An external force F(t) [N] acts on the end of the slender rod under a fixed angle of Ø [rad] with the horizontal. The slender rod is connected to a spring with stiffness k [N/m] and unstretched length lo [m] and a damper with damping constant d [Ns/m]. Note that th force exerted by the spring and damper is always directed horizontally. The gravitation acceleration g [m/s2] acts in negative vertical direction.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Question 5: Consider the mechanical system shown on the next page. Note that this
figure contains geometric information. A uniform, homogeneous, slender rod with
length L [m] and mass m [kg] can rotate about fixed point O. Its orientation is given by
angle (t) [rad], which is defined positive in counterclockwise direction. An external
force F(t) [N] acts on the end of the slender rod under a fixed angle of Ø [rad] with the
horizontal. The slender rod is connected to a spring with stiffness k [N/m] and
unstretched length lo [m] and a damper with damping constant d [Ns/m]. Note that the
force exerted by the spring and damper is always directed horizontally. The gravitational
acceleration g [m/s2] acts in negative vertical direction.
Derive the equation of motion by using
a) Newton's second law
b) Lagrange's method
c) Compare your results (is your answer correct?)
d) Determine the equilibrium point when F(t) is zero
e) Calculate the mass, stiffness and damping matrix. You don't have to fill in the
equilibrium point(s)
Transcribed Image Text:Question 5: Consider the mechanical system shown on the next page. Note that this figure contains geometric information. A uniform, homogeneous, slender rod with length L [m] and mass m [kg] can rotate about fixed point O. Its orientation is given by angle (t) [rad], which is defined positive in counterclockwise direction. An external force F(t) [N] acts on the end of the slender rod under a fixed angle of Ø [rad] with the horizontal. The slender rod is connected to a spring with stiffness k [N/m] and unstretched length lo [m] and a damper with damping constant d [Ns/m]. Note that the force exerted by the spring and damper is always directed horizontally. The gravitational acceleration g [m/s2] acts in negative vertical direction. Derive the equation of motion by using a) Newton's second law b) Lagrange's method c) Compare your results (is your answer correct?) d) Determine the equilibrium point when F(t) is zero e) Calculate the mass, stiffness and damping matrix. You don't have to fill in the equilibrium point(s)
Φ
F(t)
L/4
L/4
L/4
0
k,lo
MW
d
x a
b
g
Transcribed Image Text:Φ F(t) L/4 L/4 L/4 0 k,lo MW d x a b g
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