assignment 1
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Assignment #1 September 1, 2015 Due: September 14, 2015
1) A simplified model for a car suspension is shown in Figure 1. The road position is r(t), and the car body position is x(t). A force F is applied to the body mass. Assume r(t)=0 throughout this problem and let the force be a step function F(t) = 500u(t) [N].
(a)Solve for the resulting step response x(t) from zero initial conditions. Write an expression for the response as a function of time. Use the parameters: m = 1000 kg, k =8×104 N/m, and b =5×103 Ns/m.
(b)Use Laplace transforms to obtain the transfer function and plot the response using MATLAB.
Figure 1. A Simplified Model for a Car Suspension
2) For each of the systems shown in Figure 2:
(a) Separate the system at a node or nodes into a free body diagram to show the forces acting on each element.
(b) Use the free body diagram to develop a differential equation describing the system in terms of the indicated input and output. For each system, what is the system order?
Figure 2. Rotational & Translational Systems
3) For the values R1 = R2 = 300 kΩ, R= 10 kΩ, and C=20 μF, and assuming the op-‐amp in Figure 3 modeled as ideal with infinite gain,
(a) Calculate the pole and zero locations.
(b) Use MATLAB to plot the step response of this circuit.
(c) Describe what kind of operational amplifier is this op-‐amp?
Figure 3. Operational Amplifier