1. Consider the mass-spring-damper system shown below.m=XfX(s)(a) Calculate the transfer function G(s)F(s)(b) Assume m = 1 kg and k = 4 N/m. What value berit will result in a critically damped system?(c) For m = 1 kg, k = 4 N/m, and b = berit, derive the step response of the system.(d) Construct a Simulink model for this system and simulate its step response. Verify that the stepresponse at t=0.5 sec matches your analytical expression in part (c).(e) Determine the value of b that yields a damping factor = 0.15. Repeat parts (c) and (d).

The objective of the question is to analyze a mass-spring-damper system. We are asked to calculate…

Answered: 1. Consider the mass-spring-damper…

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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2. For the system below, find the transfer function fromfi to x (driving point receptance) and from f. to ä, (driving point accelerance). What is the acceleration response of mass m, if m; = 2 kg, m; = 4 kg, k, = 40 N/m, k =100 N/m, and k; = 200 N/m, fi(t) = 20 cos(3t) N and f:(r) = 0? WW m, WW m W
1. Consider the simplified model we discussed in class about a car on a bumpy road. The car has a mass m supported by stiffness k and damping c. The road gives a displacement excitation R(t) to the car. The transfer function from R(t) to the car displacement y(t) is Hy(s) - Y(s) R(s) cs + k ms² + cs+k (1) (a) Determine the driving point impedance ZR(s), which is the ratio of the velocity R(t) to the force acting on the wheel from the road. (b) Engineer X is testing the car in the Vehicle Dynamics Lab of a start-up company GF.com. Because of insufficient cash flow, Engineer X only has the equipment to mea- sure ZR(s), and identify the zeros and poles of ZR(s). But eigineer X wants to find the poles of Hy(s). To do so, should Engineer X use the zeros or poles of ZR(s) instead? Explain why? m y(t) R(t) Figure 1: A simple model of a car on a bumpy road
Q2: Derive the 1st order transfer function of a liquid-level system shown fig. (1) to determine the response of the outlet flow (q.(t)) to unit pulse change in the inlet flow (qin (t)). q (t) I Ih(t) 1 Fig.(1) R go (t)
The mass spring damper system shown in the figure below. Derive the transfer function relating the input displacement, u(t) to the output displacement, x(t). The parameter values are as follows: m = 1 kg, k1 = 2 N/m, c1 = 1 Ns/m, k2= 1 N/m and c2 = 2 Ns/m. What is the settling time of the system's response to a unit step input? и ki k2 WWW. ww. m C2 O 2.31 seconds O 2.67 seconds O 3,27 seconds O 4.06 seconds O o o o
2) Consider the spring-mass-damper system hanging down from a ceiling. Initially, the system is at rest. Then, we gently place another mass (M) on top the original one (m). First, please obtain the equation of motion of the mass m in the system (before we placed the other object). Assign the displacement references yourself and obtain the equation accordingly. From the equation of motion, please obtain the transfer function, G(s), between an external force on the mass m , f(t), and the displacement of the mass m, x(t). Then, please obtain the motion of the object M, using the transfer function G(s). Don't forget that G(s) belongs to the system shown on the top! To solve this, represent the force applied by the added mass (M) as a function of time. How would you describe the act of adding a mass as an external force input? Then solve for x(t). c = 10 Ns/m k = 50 N/m m = 5 kg M M = 25 kg F(s) G(s) X(s)
PLS PROVIDE ME WITH THE COMPLETE SOLUTION
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…
The state z(t) of a dynamical system is solution of equation ż(t) + aż(t) + 25z(t) = 12, with a = 7.3. Calculate the Peak time of the response.
A surface condenser deals with 12000 kg of steam per hour. Air leakage into the condenser is found to be 4 kg/hr. The vacuum and temperature at the air pump suction are 700 mm of Hg and 36°C respectively. The barometric pressure is 760 mm Hg. Compute the volumetric capacity in m'/min of wet air pump.
:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k

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