I Need Help on this. Full Steps. Problem 2: Consider a stainless steel solid sph

Question

I Need Help on this. Full Steps.

Problem 2: Consider a stainless steel solid sphere, with mass density p 7890 kg/m3 and radius r 0.25 m. The mass is attached to the top of a coil spring, also made of stainless steel. The radius of the spring is R 0.1 m. The wire diameter is d. 0.03 m. The number of coils is n 5. The shear modulus for stainless steel is G 79.3.10 Pa. A piston damper is placed inside the coil. The piston diameter is D 0.05 m. The piston has a single hole of diameter de 0.004 m and length L 0.02 m. The piston is filled with motor oil of viscosity 0.32 N-s/m m Coil spring 1. Calculate the mass m of this sphere. 2. Calculate the stiffness k of the spring. 3. Calculate the damping coefficient c of the damper. 4. Find the ODE goveming the vertical oscillations x(t) of the mass, assuming that no extemal force is applied. 5. Calculate the angular natural frequency eub of the system. 6. Calculate the damping ratio gof the system. Is the system overdamped, underdamped or critically damped 7. Calculate the damped angular frequency and damped period Ta of the system. 8. The mass is pulled from its position of equilibrium to a heightx(0) 0.1 m (upward). The mass is then released with an initial speed i(0)30m/s. No external force is applied. Find the expression for 9. Using your answer in 8, calculate x(0) x(T/2), x(Ta, x(3T/2), x(2Ti) and sketch x() from t 0to 2Ta 10. In MATLAB, create a simulink model that calculates the vertical displacement of the mass. Plot the vertical displacement from 0to 2T

Explanation / Answer

1) Mass of spring = 7890*(4/3)*3.14*(0.25)^3 = 516.1375 kg

2)

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