Question

For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each motion and transfer functions (FC),T()) (b) With m - 1 (kg),c4(N/m/s), k 20(N/m) and a unit step input (y(t) - us(t)), find 1(s) X2 x1(t) and x2) (c)(i) Draw the unit step input, x(t) and x2(t) in a figure by using Matlab (ii) Draw the unit step input and x1(t) with c= 0,4,9 in a figure by using Matlab X1(t) x2(t) Fig. 2. Two suspensions Consider a lever system as shown in Fig. 3. 3. (a) Derive the equation of motion and the traP), assuming small e(s) F(s) displacements and the zero initial conditions. (b) When does the lever system oscillate? し2 Fig. 3 4. Obtain the expression for the oscillating frequency (f) (Hz) for the pulley system shown in Fig. 4. Assuming the moment of inertia (I) is m2 R2' ,1 Fig. 4 5. For the rotational mechanical system shown in Fig. 5, find the transfer functions T(s) 1 N-m/rad Tt) θ2(1) I kg-m2 1 N-m-s/rad 1 N-m-s/rad 1 N-m-s/rad Fig. 5 θ2(s)/T(s), for the rotational mechanical system Find the transfer function (G(s) shown in Fig6 500 N-m-s/rad 100kg-m2 Na 25 T0) 3 kg-m2 00 N-m/rad 200kg-m Fig. 6 7. In the system shown in Fig. 5, the inertia, J, of radius, r, is constrained to move only about the stationary axis A. A viscous damping force of translational value f exists between the bodies J and M. If an external force, f(t), is applied to the mass, find the transfer function, G(s) (s)/F(s). fRt) Fig. 5 8. There is an electromagnetic speaker shown in Fig. 6. Speaker enclosure Magnet Coil Fig. 5 (a) Find the transfer function (X/V) relating the diaphragm displacement (x) to the applied voltage (v), as considering the following conditions 1) The diaphragm can be schematically modeled to a mass-spring-damper mechanical system with a spring (k), a damper (c), and a mass (m). 2) The voice coil motor generates a force based on the Lorentz force (f nBil Kyi) and can be schematically modeled to an electrical system with a resistor (R), a inductor (L), and an -EMF voltage. Kf: force constant, K:-EMF constant (b) As ignoring the inductance of the voice coil motor and assuming all constant values to 1, obtain the displacement (x(t)) with an unit step input (u()) as the input voltage (v). 9. There is a motor and gear system as shown in Fig. 6 (a) Find transfer functions, G1-θ3(s)/7, (s), G2(s)-θ3(s)/Ea (s), and G2 (s)-0,(s)/ (Up(t,-Kbddtt),T(t)-Kia(t), La ~0), assuming θ-0,, and Ea(s) T, gear ratio-N. ст θ3 02 La Ra Rotor Armature vT) ealt) circuit ialo θ(r) Fig. 6 10. Consider the system shown in Fig. 7 (a) Obtain the transfer function (G(s)-x(s)%, (s). eal Motor N 10 J-1 kg-m2 RN-m-s/rad N2 -20 Ideal gear 1:1 Radius 2 m M-1 kg For the motor: ru) Da 1 N-m-s/rad Ky = 1 V-s/rad Fig. 7

Answer 1

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