suspension or You are requested to design an aut 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 = 2500 kg = 320 kg = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁₂ M₂ Rn Ka x₁(1) x₂(1) Tire

this question about control systems for mechanical engineering. i will send two times because there are 4 parts a b c d. if u can a and b now, i will be happy. thank you!

HELP!!! ASAP!!! DIFERENTIAL EQUATION

Vibration Topic. Please help with the solution with neat answer and correct units. Will upvote to answer. Thanks

A structure has a mass of 10 kip/g and a stiffness of 10 kip/in. The acceleration of gravity, g, is 386.1 in/s2. What is the value of damping assumed by the code?

A spring system is shown here: k₁ 3 Ę k3 2 K₂ www ma 4 Ę₂ Part 1: For this specific system, develop the: a. Global stiffness matrix . b. Boundary condition vector • c. Load vector • d. Reduced system of equations • e. Reaction force equations (i.e., the equations eliminated by the boundary conditions) Part 2: Given: k1 = 70 N/mm, k2 = 110 N/mm, k3 = 165 N/mm, F1 = 150 N, F2 = 100 N, and nodes 1 and 3 are fixed; calculate the: a. Global stiffness matrix b. Displacements of nodes 2 and 4 c. Reaction forces at nodes 1 and 3 d. Spring force in each of the springs

Find the differential equation of the mechanical system in Figure 1(a) To obtain the differential equation of motion of the mass and spring system given in Fig. 1. (a) one may utilize the Newton's law for mass and spring relations defined as shown in Fig. 1. (b) and (c) use f = cv for viscous friction, where v is the velocity of the motion and c is a constant. Z/////// k M F. F, F F F, F, k EF=ma F = k(x, - x,) = kx (b) (c) Figure 1: Mass-spring system (a), Force relations of mass (b) and spring (c)

2. Below is a picture of a car suspension system with additional springs (in red) added in series. Assume the car remains "level" (i.e. no rotational motion of the car body, only vertical motion). The original springs are ks modeling tire/road interaction). The car mass is m = 2,000 kg. 20, 000 N/m (the suspension spring), and kt 100, 000 N/m (the spring %3D The springs are all in equilibrium when d = 0.4 m. Ignore gravity in this problem. The point of the additional spring k is to make the ride more "bouncy" (some people like it that way). However, you need to make sure the car does not "bottom out" (i.e. hit the bump). It is known that when the springs are unstretched/uncompressed, the marimum vertical velocity can be is 1 m/s. What is the minimum value of the spring constant k (of the additional red spring) so that the car does not hit the bump during its vertical oscillations. Hint: Use energy balance. kis k's kt Figure 4: Simplified car model with upper springs representing…

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