Question

differential equations:

a mass of 2kg stretches a spring 1m. the mass is in a medium that exerts a viscous resistance of 8 newtons when the velocity of the mass is 2m/sec. the mass is stretched from its equilibrium position 1m and then set in motion with a downward velocity of (3sqrt(3) - 1) m/sec. Let g=10 m/sec^2

a)state and solve the initial value problem for u(t), the displacement of the mass from its equilibrium position

b) what is the limit to the solution found in part a as t approaches infinity? why?

c) how many times does the mass pass through its equilibrium position? why?

Answer 1

Any query in any step then comment below.

mer Kamer 20 - 20 8 = 4 co "+ un'tou e o u"+ 2u't louw Dr - 27 J4-40 -22 61 0 - 3 ulte t ( G cos(3+) + (2 sin (3+)) allole 33 - - G+ 362 =353-1 & Tulta et (cos(3t) + 53 sih (st)) ( in ultir o u ta infinite times

In part b) .. as amplitude of the displacement funtion u(t) goes decreases exponential... So it becomes 0 when t approaches to infinity...

In part C) ... As u(t) is periodic function ...so it moves ups and down infinite te about equilibrium position...