Figure 1 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyroscope" for measuring angular v

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Figure 1 Shows A Lumped Parameter Representation Of A Concept For A Mems Tuning Fork Gyroscope For Measuring Angular V 1 (298.83 KiB) Viewed 39 times

Figure 1 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 k = 3.9 / k₂ = 4.5 M, and k3 2.2. The system friction is represented by three ideal lumped dashpot elements b₁ = 0.7 b₂ = m² m N = 2.1 and b3 N m/s' m/s' N 1.8 Two external forces f₁ = 92 N and f₂ = 18 N are applied to masses m₁ = 10 kg, m/s' m₂ = 16 kg, and m3 = 7 kg, respectively. Derive the mathematical model of the MEMS gyroscope. To do so, you must a) Draw the free body diagram for the system. [3 marks] b) Use Newton's 2nd law to find the equations in the proper format. [6 marks] c) Substitute the values and find the final answers. [1 marks] Assume x₁ > x3 (spring k, is compressed), x3 > x₂ (spring k₂ is compressed) and positive direction is to the right. You are required to show all the steps involved in finding your final answer, even the smallest details. Make sure in your final answer, all numerical values are substituted and equations are simplified to the simplest form. b₁ fi C K₂ www m₁ m₂ www k₁ O O K3 www b₂ m3 O O Figure 1 schematic of the tuning fork gyroscope system Solution Provide your step by step solution here. Note that only providing the correct final answer does not guarantee a full mark for the question! f₂ b₂ m