A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external for

Question

A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10*sin(t/2) N (newtons) and moves in a medium that imparts a viscous force of 2 N when the spee dof the mass is 4 cm/sec. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/sec, formulate the initial value problem describing the motion of the mass and then solve the initial value problem. Identify the transient and steady-state parts of the solution and use Maple to plot your soluion.

Explanation / Answer

(i) determine the position y of the mass at any time t.
my" + y' + ky = g(t)

m = 5

g(t) = 10 sin(t/2)

L = 10 cm = 0.1 m

g = 9.8 m/s2

k = mg/L = 49/0.1 = 490

Fd = -v where Fd = -2N when v = 4 cm/s = 0.04 m/s

= 2/0.04 = 50

ODE:

5y" + 50y' + 490 y = 10sin(t/2)

Initial conditions:

For clear explanation use this link:

http://www.math.umass.edu/~tanguay/331/331spr10hw18sol.pdf

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