A steady force of 40N is required to lift a mass of 2kg vertically through water at a constant speed of ms^?1. Assuming that the effect of viscosity can be described by a force proportional to velocity, determine the constant of proportionality. (The effect of buoyancy should be neglected.) The same mass is then suspended in water by a spring with force constant k = 100N m^?1. ?Determine the equilibrium extension of the spring. The mass released from rest 20 cm below its equilibrium position at time t = 0. Show that it will vibrate about the equilibrium position according to an equation of the form

and determine y and w₀ for the system.

Given that x = A exp (-?t) cos (wt + ?) is a solution of this equation if w² = w²₀ ? y², calculate the period of oscillation of the system, and sketch the variation of x as a function of time.

Transcribed Image Text:

d'x/dr? + 2y dx/dı + wóx = 0,