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

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*** *Show your correct and complete solution neatly. ASAP! Thanks. Given the vibrating system below: K4 Y(t) =Ysin30t where fc: = 30 and K1 Y=20mm Find the following: m C3 C2 C5 C4 M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2= 40 Ns/m C3= 35Ns/m C4-15 Ns/m C5=10 Ns/m 1. Type of Damping 2. Equation of motion x(t). Assume Initial conditions for displacement and velocity. 3. Graph 2 cycles of the vibrating system. You can use third party app for this.

Consider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. Pell (P2 R2 P1 Pa ¡P3 R1 P4 L2 Li Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form. b. If you were to consider the input to the system to be the difference between the pressure on 0(s) either side of the piston, write the transfer function for the displacement of the piston: AP(s) Xj = 0 c. Develop the state equations for this system if the state variables are:

Calculate the natural frequencies and vibration modes of a free-vibrating 2-GDL spring-mass system, using the matrices of this system presented below. mass matrix stiffness matrix [":] m 2k -k M K: %3D т ーk 2k

1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.

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…

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SUBJECT (VIBRATION) PLS USE THIS MATRIX NUM SIR (AD 200153)