Consider a damped, forced mass/spring system. Let t denote time (in seconds) and let x(t) denote the position (in meters) of the mass at time t, with x = 0 corresponding to the equilibrium position. Suppose the mass m = 1 kg, the damping constant c = 3 N·s/m, the spring constant k = 2 N/m, the external force is F (t) = 20 cos(2t), the initial position x(0) = 1 m, and the initial velocity x′(0) = 2 m/s. a. Find the position function x(t). b. What part of the solution is the transient part and what part is the steady-state part? An RLC circuit contains in series a resistor R = 3 Ω, an inductor L = 1 H, and a capacitor C = 0.5 F. The current I(t) is provided by a source with emf E = 20cos(2t) Volts, where t is the time. Find the steady-state current Ip that develops after a long time (theoretically when t → [infinity]). For the differential equation y′′ + 4y = 2 tan(2x), solve its homogeneous part. Then use variation of parameters to find a particular solution yp.

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.