In Figure 3, a wheel (solid disk) of known mass m and moment of inertia I, rolls without slipping and is attached to a spring and a damper that are connected to a fixed support. The point P is approximately vertical over the center of the disk at point O, which means you can use the small angle assumption. There is an input torque from a motor, T(t). 1 m, lo=mR² 2 R 0 P T(t) Figure 3: Schematic of the mechanical system to model in Problem 4. Your tasks: A Draw the free body diagram of the disk B Derive the equation of motion of the disk in terms of the rotation angle, 0. C Does the location of the input moment 7 make a difference in your strategy on how to go about your analysis? Why or why not

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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In Figure 3, a wheel (solid disk) of known mass m and moment of inertia I, rolls without slipping and is attached to
a spring and a damper that are connected to a fixed support. The point P is approximately vertical over the center
of the disk at point O, which means you can use the small angle assumption. There is an input torque from a motor,
T(t).
1
m, 10 = = mR²
lo
R
b
Q
T(t)
k
Figure 3: Schematic of the mechanical system to model in Problem 4.
Your tasks:
A Draw the free body diagram of the disk
B Derive the equation of motion of the disk in terms of the rotation angle, 0.
C Does the location of the input moment 7 make a difference in your strategy on how to go about your analysis?
Why or why not?
Transcribed Image Text:In Figure 3, a wheel (solid disk) of known mass m and moment of inertia I, rolls without slipping and is attached to a spring and a damper that are connected to a fixed support. The point P is approximately vertical over the center of the disk at point O, which means you can use the small angle assumption. There is an input torque from a motor, T(t). 1 m, 10 = = mR² lo R b Q T(t) k Figure 3: Schematic of the mechanical system to model in Problem 4. Your tasks: A Draw the free body diagram of the disk B Derive the equation of motion of the disk in terms of the rotation angle, 0. C Does the location of the input moment 7 make a difference in your strategy on how to go about your analysis? Why or why not?
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