Consider a car suspension, modeled as a mass/spring/damper system (mass m, stiffness k, damping b). Suppose the height of the chassis is lo at rest, the height of the terrain below the driver varies as h(t), and the height of the chassis is denoted lo + y(t). (i.e., spring deflection away from rest is y(t) - h(t)). Y(s) (a) Give the transfer function G(s) = H(S) (b) Suppose the ground follows an oscillatory profile h(t) = A cos(wx(t)) with magnitude A (in meters) and frequency w (measured in radians per meter). Suppose the car is traveling at a constant forward speed v. Using a frequency response analysis strategy, give the amplitude of oscillations experienced by the driver at steady state as a function of m, k, b, A, w, and v. Hint: You can't simply consider |G(iw)| to get the amplification in this case. (c) Suppose the ground varies by A = 5cm, w = 25 rad/m, and you are driving at v = 15 m/s. Using your answer to part (b), what amplitude of oscillation is felt by the driver when m = 1350 kg (the approximate mass of a Honda Civic), k = 200, 000 N/m, and b= 10, 000 Ns/m. (d) Use MATLAB to graph the Bode plot for G(s) (use the command bode) using the same k, b and m as part (c). Turn in your graph. From looking at the Bode plot, is the system underdamped or overdamped? Explain your reasoning. (e) Repeat part (c), rather than using the formula from part (b), this time use your Bode plot to obtain the answer. (f) In your opinion, is this suspension system effective at its job of dampening vibrations?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:2. Consider a car suspension, modeled as a mass/spring/damper system (mass m, stiffness k, damping b). Suppose the height of the chassis is lo at rest, the height of the terrain below the driver varies as h(t), and the height of the chassis is denoted lo + y(t). (i.e., spring deflection away from rest is y(t) – h(t)). 2 (a) Give the transfer function G(s) = H(s) · = (b) Suppose the ground follows an oscillatory profile h(t) A cos(wx (t)) with magnitude A (in meters) and frequency w (measured in radians per meter). Suppose the car is traveling at a constant forward speed v. Using a frequency response analysis strategy, give the amplitude of oscillations experienced by the driver at steady state as a function of m, k, b, A, w, and v. Hint: You can't simply consider |G(iw)| to get the amplification in this case. (c) Suppose the ground varies by A = 5cm, w = 2 rad/m, and you are driving at v = 15 m/s. Using your answer to part (b), what amplitude of oscillation is felt by the driver when m = 1350 kg (the approximate mass of a Honda Civic), k 200,000 N/m, and b= 10,000 Ns/m. = (d) Use MATLAB to graph the Bode plot for G(s) (use the command bode) using the same k, b and m as part (c). Turn in your graph. From looking at the Bode plot, is the system underdamped or overdamped? Explain your reasoning. (e) Repeat part (c), rather than using the formula from part (b), this time use your Bode plot to obtain the answer. (f) In your opinion, is this suspension system effective at its job of dampening vibrations? DI

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