Problem 10 Two Degree of Freedom-Free Undamped Vibrationanstant.Car masskmX2Car springM22kM2Tyre mass2mTyre stiffneX22kFigure P10 - Two-degree-of-freedom model of avehide suspension systemFigure P11Problem 104 sighty more sophisticated model of a vehicle suspension system is given in FigurePI0. Write the equations of motion in matrix form. Calculate the natural frequenciestor k;=10° N/m ; k2=10* N/m ; M2=50 kg ; M1=2,000 kg.

Answered: Image /qna-images/answer/fdc2b923-6b28-4b54-b6e8-8add1f716ffa.jpg

Problem 10 1 sightly more sophisticated model of a vehicle suspension system is given in Figure P10. Write the equations of motion in matrix form. Calculate the natural frequencies trk=10° N/m ; k2=10* N/m ; M2=50 kg ; M1=2,000 kg.

Problem 10 1 sightly more sophisticated model of a vehicle suspension system is given in Figure P10. Write the equations of motion in matrix form. Calculate the natural frequencies trk=10° N/m ; k2=10* N/m ; M2=50 kg ; M1=2,000 kg.

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

See similar textbooks

Similar questions

Q1 A vibration model of a machine system that consists of three levers connected by lightweight linkages (represented by spring) is shown in Figure Q1. Each lever has a length, L with the distance of linkage from pivot point is given as ´a’. Important: Please provide the final answer equation of motion in the matrix form of unknown m, k, a and L. (a) By using Lagrange equation, determine the equation of motion of the system by considering 0,, 02 and 03 are very small. (b) Prove the answer from Q1(a) by using Newton's second law. Use a free body diagram to support the answer.
Consider the following spring system. ////// m, _with spring constants c = 3 Assume down is the positive direction. Write the stiffness matrix K = 3. • Compute the external force which causes the displacement u = Force =
A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where ky is the suspension stiffness, my the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 24.4 kN/m, m₁ = 257.5 kg, k₂ = 83.2 kN/m, and m₂ = 28.8 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring k₂ Tire stiffness Figure Q2 Answer: m₂ Wheel mass
Q1: (Section A) Considering single degree undamped vibration system and Newton's equation as follow: më +kx=0; find the solution of the displacement equation [(t)=Cietwnt+C2e-lwn] for the case with: Wn = 2 rad/s, x (0) = 1 mm, and x(0) = v5 mm/s. (Section B) Given the matrix equation of motion of a two degree-of-freedom system 3m 2k - k = 0 X2 + as: -k 4k m Determine (a) the natural frequencies, (b) the modes shapes.
Consider the following spring system. m, C2 C3 with spring constants c = |2 m2 Assume down is the positive direction. Write the stiffness matrix K = %3D 23 • Compute the displacements caused by the external forces f = -21 Displacement =
Problem 5 Consider the two-mass system connected by two springs. Let coordinates x, and x, be such that when they are both zero, the springs are at their natural lengths. Write down the equations of motion. Use the Matlab command ode45 to solve the initial value problem with parameters m = m2 = k, = 1, k2 = 10 and initial conditions x,(t = 0) = *,(t = 0) = *,(t = 0) = 0, x2(t = 0) = 0.1 for te [0,67]. Plot x, and x2 as functions of t. Submit your plot as well as codes.
Crack AB of a slider crack mechanism shown in Figure 2 rotate at a constant speed of 300 rpm in clockwise direction. The connecting rod BC has a length of 1 m and incline at 45° to vertically positioned piston C. B 1 m 0.2 m 459 Figure 2: Slider crank mechanism 3.1. Draw the displacement diagram of the mechanism shown in Figure 2 to scale. 3.2. Use a vector diagram to determine the velocity of the piston C and connecting rod BC. 3.3. Calculate the acceleration of piston C and the angular acceleration of connecting rod BC.
For the mechanism shown below, use the graphical position analysis to specify the value(s) of 02 when the linear speed of link 6 is zero. The parameters of each link length is: L2 = 3 cm, L3 =10 cm (O₂B), L5 = 4 cm, L σ₂³ = 5 cm. ////////////////// 5 B 4 0₂ 2 3 A₂ on 2 and 4 A3 on 3 10.5 cm
A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where k, is the suspension stiffness, m, the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 22 kN/m, m₁ = 304.3 kg, k₂ = 82.2 kN/m, and m₂ = 36.1 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring m₂ k₂ Tire stiffness Figure Q2 Answer: Wheel mass
The members of the mechanism are pin connected. The spring is unstretched when 0 = 0°. Neglect the mass of the links. A vertical force of 800 N acts at A. a. Draw how the virtual displacement on this mechanism would look like. b. Write down x and y coordinates as a function of the angle 0 with the respective derivative of the virtual displacements expressions. c. Write the virtual work equation d. Determine the angle 0 for equilibrium k = 6 kN/m 1 m 1 m 1 m 800 N Dwwww
Find the Frequency Ratio, Displacement, Transmissibility Ratio, Absolute displacement of the mass, Type of Damping, and Equation of motion x(t). Assume Initial conditions for displacement and velocity. Graph 2 cycles of the vibrating system.
Figure Q9 shows part of a system with many degrees of freedom. Write the equation of motion for m₂. Specify the assumptions that you may need to consider in determining the relative displacements and subsequent spring forces. ■ ■ ■ Kn-1 i M Fn-1 Kn Juny mn-1 mn kn+1 Fn mn+1 Kn+2 n