Degree of Freedom of a mechanical system is the number of dependent parameters that define its configuration

Explain the concept of system reliability and its significance in engineering applications.

I am struggling with a, b,c,d

Q)(a) A spring and mass system is shown in Figure P1.8. Assume that the rotation is small so that the spring deflects horizontally and ignore mass of the rod. Determine the frequency of vibration. (b) If total mass of the rod is m0 , how it will affect the frequency of vibration?

Geochemical Box Models - please use same terminology found in question Consider an element X exchanging between two geochemical reservoirs A and B. Let MA and MB be the masses of X in reservoirs A and B, respectively; let tA and tB be the residence times of X in reservoirs A and B, respectively. Further let M = MA + MB be the total mass of X in the two reservoirs combined. Consider a situation where additional mass M' is injected into reservoir A at time t=0 increasing the total amount of element X in the system from M0 to M1, with no further injection at later times; further assume that tA >> tB, that the total mass in the altered system is M1 = M0 + M', and that M0 << M'. Give an expression for MB(t) as a function of M1, tA, tB, and t. What is the characteristic time for MB to approach steady state? What is the characteristic time for MA to approach steady state?

Heat is being generated in a fuel element at a volumetric heat generation rate of q′′′ = 1300 kW/m3. The fuel element is a rectangular parallelepiped of thickness 2 cm with a height of 2 m and width of 1 m. The fuel thermal conductivity is k = 3.5 W/m·C. Find the rate of heat transfer from the fuel element at steady state condition. [Ans.: 52 kW].

1) Obtain a state space model of the system. 2) Given m =1 kg, k = 1 N/m and b = 1 N.s/m is the system Controllable? 3) For what values of k,m,b the system is stable? Explain your answer?

Material Mechanics

Thermodynamics

The rapid progress of engineering design and information technology has caused difficulties in analyzing system reliability. Because of the increased complexity in system reliability structure (component/subsystem interfaces), many unexpected failure modes could occur, and their behaviors are interdependent. At a system’s design and development stage, the main challenge in analyzing a complex system is the failure uncertainty introduced by the incomplete knowledge of the system. This makes it hard to decompose system reliability into subsystem/component reliability in a deterministic manner, such as series or parallel systems. As a result, some common reliability analysis tools such as fault tree (FT) and reliability block diagram (RBD) become inadequate. Do you agree, why or why not? Are there any other approaches to system reliability assessment beside these tools at the early system’s design and development stage (what are these approaches)?