1. A spring mass system serving as a shock absorber under a car's suspension, supports the M = 1000 kg mass of the car. For this shock absorber, k = 1 x 10°N/m and c = 2x 10° N s/m. The car drives over a corrugated road with force F = 2 x 10' sin(@t) N . Use your notes to model the second order differential equation suited to this application. Simplify the equation with the coefficient of x'" as one. Solve x (the general solution) in terms of w using the complimentary and particular solution method. In determining the coefficients of your particular solution, it will be required that you assume w -1 x o or 1- w 2 -w. Do not | use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.

1. A spring mass system serving as a shock absorber under a car's suspension, supports the M = 1000 kg mass of the car. For this shock absorber, k = 1 x 10°N/m and c = 2x 10° N s/m. The car drives over a corrugated road with force F = 2 x 10' sin(@t) N . Use your notes to model the second order differential equation suited to this application. Simplify the equation with the coefficient of x'" as one. Solve x (the general solution) in terms of w using the complimentary and particular solution method. In determining the coefficients of your particular solution, it will be required that you assume w -1 x o or 1- w 2 -w. Do not | use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter6: Forced Convection Over Exterior Surfaces

Section: Chapter Questions

Problem 6.32P

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1. Aspring mass system serving as a shock absorber under a car s suspension, supports the M = 1000 kg mass or the car. For this shock absorber, k = 1x 10°/m and c = 2x 10' N s/m. Tne car drives over a corrugated road with rorce F = 2x 10' sin(@t) N. Use your notes to model the second order difrerential equation suited to this application. Simplity the equation with the coerricient of X" as one. Soive X (tne general solution) in terms or @ using the complimentary and particular solution method. In determining the coernicients of your particular solution, it will be required that you assume o -1xo or 1- w x -m. Do not use Matiab as its solution will not be identiriable in the solution entry. Do not determine the value of W. You must Indicate In your solution! 1. Tne simpliried dirrerential equation in terms or the displacement X you will be solving 2. Ine m equation and complimentary solution Xe 3. Tne choice ror the particular solution and the actual particular solution Xp 4. Express…
1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…
You are requested to design an automotive suspension or shock absorber system. In order to simplify the problem to one dimensional multiple mass-spring-damper system, a quarter vehicle model is used. The system parameters and free-body diagram of such system is shown below. M₁: Automobile body mass M₂: Wheel and suspension mass K₁: Spring constant of suspension system K2: Spring constant of wheel and tire B: Damping constant of shock absorber (a) Obtain the transfer function of X₁ (s) F(s) T₁(s) = = 2500 kg = 320 kg and T₂(s) = = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁ M₂ X₁ (s) - X₂ (S) F(s) in terms of the parameters of mass, damper and elastance (M, B and K). (b) Express the T₁ (s) and T₂ (s) with numerical values. c) Plot the x₁ (t) and x₁ (t) = x₂(t) outputs of this passive suspension system for the input torque f(t) = 2,000 N. fit) K₂ x₂(t) -Tire
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First Order Differential Equations are inherent in almost all aspects of engineering, e.g., electronics (RC/RL circuits or charge/discharge of capacitors), thermodynamics (i.e., Newton’s Law of Cooling), mechanical systems (stress/strain) etc. In fact, virtually anywhere there are time varying dynamics. You need to demonstrate how different engineering systems models are used to solve them using first-order differential equations.
Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.
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A rectangular tube of outer width w = 7.5 m, outer height h = 5 m and thickness t = 0.17 m experiences bending through the x axis. What is the moment of inertia of the cross-sectional area In? y -- X MATLAB input variables: format shortEng W = 7.5; h = 5; t = 0.17; moment of inertia I, = m4