Amass weighing 32 lb stretches a spring 4 ft. the mass is attached to a viscous damper with a damping constant of 4 lb2s/ft. the mass is pushed upward, contracting the spring a distance of 1 ft, and then set in motion with a downward velocity of 4 ft/s. (a) determine the position y of the mass at any time t. (b) find the (or quasi) frequency, period, phase and amplitude of the motion, that is to find wo, t, δ and r from y(t) = rect cos(wot-5). (c) if there is an external force of f(t) 26et lb, in m" ky f(t), what is the general solution (not considering the initial condition)?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes. t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

If an astronaut takes an object to the moon the following is true (choose only one). a the mass will change but the weight will be the same. b both the mass and the weight of the object will be the same. c the weight will change but the mass will be the same. d both the mass and the weight of the object will change.

8.29 two streams containing pyridine and acetic acid at 25°c are mixed and fed into a heat exchanger. due to the heat-of-mixing effect, it is desired to reduce the temperature after mixing to 25°c using a stream of chilled ethylene glycol as indicated in the diagram. calculate the mass flow rate of ethylene glycol needed. the heat capacity of ethylene glycol at these conditions is approximately 2.8 kj/(kg k), and the enthalpy change of mixing (δmixh) is given below.