For the following system, a) obtain the equivalent system b) derive the equation of motion using Energy Method, where, KE=½ m x², and PE=½ k x², c) find the natural frequency.
The data show the population (in thousands) for a recent year of a sample of cities in South Carolina. 26 26 15 29 69 21 30 29 26 20 38 85 19 23 29 25 111 47 49 108 30 38 ?? ?? 13 19 30
PROBLEM 3 (30 points)Due to slipping, points A and B on the rim of the disk have the velocities shown. Determine the velocity of point D at this instant.1. Using the relative equation 2. Using the IC method
a. Determine analytically and plot the individual and total system response magnitude ratios MA, MB, and Msys (w) versus frequency for the range 0 – 100 krad/sb. If the steady-state input signal x(t) = 3sin( wt) + 2, with x unitless, t in seconds and o =20 krad/s, determine the steady-state output signal z(t).
Problem 1, 19pts An initially straight beam is bent into a circle with radius R as shown in the figure. Material fibers that are perpendicular to the axis of the undeformed beam are assumed to remain perpendicular to the axis after deformation, and the beam's thickness and the length of its axis are assumed to be unchanged. Under these conditions the deformation can be described 2? = (R-X?) sin(¹), 2?-R- (R-X2?) cos( (a) Calculate the deformation gradient field in the beam, expressing your answer as a function of X?, X?,, and as components in the basis e?,e?, e shown. (b) Calculate the Green Lagrange E* strain field in the beam. (c) Calculate the infinitesimal strain field E in the beam. (d) Compare the values of Lagrange strain and infinitesimal strain for two points that lie at (X? = 0, X?=h) and (X? = L, X?-0). Explain briefly the physical origin of the difference between the two strain measures at each point. Recommend maximum allowable values of h/R and L/R for use of the infinitesimal strain measure in modeling beam deflections. (e) Calculate the deformed length of an infinitesimal material fiber that has length lo and orientation e, in the undeformed beam. Express your answer as a function of X?.
4. The figure indicates a two-dimensional diffuser that produces no net turning of the flow. For the geometry shown, calculate the overall stagnation pres- sure ratio for a flight Mach number of 3.0. Neglect all losses except those occurring in the shocks. Would this diffuser be easy to start?
Question 1 a) Define JIT and Lean Manufacturing and contrast the similarities and differences between the two. Discuss why the ‘Traditional approach’ is more intuitive and what approaches are needed to move toward a JIT scenario? b) Critically appraise five of the nine Just in Time (JIT) techniques e.g. reduction of set up time, TPM etc. highlighting what they are and how they would be implemented c) Describe a tool or technique which can be used to analyse and improve the performance of manufacturing systems e.g. Rank-order clustering, Ishikawa diagrams, Value Stream Mapping Root cause analysis, Pareto Analysis etc. Explain the basic principle behind the technique, how it would be applied and the potential benefits/inhibitors to implementation.
Problem 2. (a) A tachometer has an analog display dial graduated in 5 rpm increments.The user manual states an accuracy of 1% of reading. Estimate the uncertainty in the reading at 10 rpm, 500 rpm and 5000 rpm. (b) A certain obstruction type flow meter (orifice, venturi, nozzle), shown in the following figure is used to measure the mass flow rate of air at low velocities. The relationship describing the flow rate is: \dot{m}=C A \sqrt{\left[\frac{2 g_{c} p_{1}}{R T_{1}}\left(p_{1}-p_{2}\right)\right]} where, * C = empirical-discharge coefficient. * A = flow area * T1 = upstream temperature * R = gas constant for air * Pi and p2 = upstream and downstream pressures, respectively. Calculate the percent uncertainty in the mass flow rate for the following conditions:
Provide some examples of different types of energy rates and demand charges in use in the US. Need to complete the question in 500 words and MLA referencing
