4.87 Consider again the model of the vibration of an automobile of Figure 4.25. In this...
An automobile suspension system is modeled as a 2-DoF
vibration system as shown in Figure below
Derive the equation of motion
Determine the natural frequencies of the automobile
with the following data
Mass (mm) = 1000kg1000kg
Momen of inertia (ImIm) = 450kgm2450kgm2
Distance between front axle and C.G. (LfLf) =
1.2m1.2m
Distance between rear axle and C.G. (LfLf) =
1.5m1.5m
Front spring stiffnes (kfkf) = 18kN/m18kN/m
Rear spring stiffnes (krkr) = 17kN/m17kN/m
Front damper coefficient (cfcf) =
3kNs/m3kNs/m
Rear damper...
Figure 1 shows the simplified model of a quarter vehicle suspension. In Homework #1, we have derived the equations of motion for the vehicle mass m. Now the vehicle is traveling on a wavy road at the constant velocity u. Use the dynamic model in Homework #1. z(t) v constant y = Asin ( 2 *) Figure 1 (a) Determine the most unfavorable speed v if the system is undamped, i.e.c0. (b) Derive the system response z(t) and plot the...
icen Consider the wing vibration model of Figure 4.20. Using the vertical motion of the point of attachment of the springs, x(t), and the rotation of this point, ?(t), determine the equa- tions of motion using Lagrange's method. Use the small-angle approximation (recall the pendulum of Example 14.6) and write the equations in matrix form. Note that G denotes the center of mass and e denotes the distance between the point of rotation and the cen??????????????????? ter of mass. Ignore...
Additional Prob. 1: Consider a two-mass quarter-car model of a suspension system as shown in figure. The system properties are: m1 = 240 kg, m2 = 36 kg, k1 = 1.6 x 104 N/m, k2 = 1.6 x 105 N/m, C1 = 98 N-s/m a. Find equations of motion for the system. c. If y(t) is a unit step function, find the responses X1 and x between 0-10 s using Simulink. m m,
Consider the mass M subject to periodic forcing P(t) A sin wt where A 0.3 and e is a small parameter. The mass is attached to a spring with stiffness k and dashpot with damping coefficientc to model the stiffness and damping of the structure. Resting atop the idealized structure is vibration damper consisting of a mass ma, spring ka, and dashpot ca, as shown in Figure 1. The goal is to make the appropriate choice of the parameters ma,...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
Question 6.3
6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...