Question 11: Figure 5 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyroscope" for measuring angular velocity. Displacements X₁, X2, and x3 are absolute positions of the respective masses and are measured from their static equilibrium positions where there is no deflection in the springs. The system friction is represented by three ideal lumped dashpot elements b₁,b2, and b3. Two external forces f₁ and f₂ are applied to masses m₁ and m₂, respectively. Derive the mathematical model of the MEMS gyroscope.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Question 11: Figure 5 shows a lumped-parameter representation of a concept for a MEMS
"tuning fork gyroscope" for measuring angular velocity. Displacements X₁, X2, and x3 are
absolute positions of the respective masses and are measured from their static equilibrium
positions where there is no deflection in the springs. The system friction is represented by three
ideal lumped dashpot elements b₁,b2, and b3. Two external forces f₁ and f₂ are applied to masses
m₁ and m₂, respectively. Derive the mathematical model of the MEMS gyroscope.
x3
Leto,
fi
k₁
m3
k3
x1
m1
x2
m₂
f₂
b2
Transcribed Image Text:Question 11: Figure 5 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyroscope" for measuring angular velocity. Displacements X₁, X2, and x3 are absolute positions of the respective masses and are measured from their static equilibrium positions where there is no deflection in the springs. The system friction is represented by three ideal lumped dashpot elements b₁,b2, and b3. Two external forces f₁ and f₂ are applied to masses m₁ and m₂, respectively. Derive the mathematical model of the MEMS gyroscope. x3 Leto, fi k₁ m3 k3 x1 m1 x2 m₂ f₂ b2
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