Question

A 16​-lb weight stretches a spring 16 ft. The​ spring-mass system is in a medium with a damping constant of 1.5 ​lb-sec/ft, and an external force given by

f (t)= 3+e^-3t ​(in pounds) is being applied. What is the solution function describing the position of the mass at any time of the mass is released from

1ft below the equilibrium position with an initial velocity of 2 ​ft/sec downward?

Answer 1

We know the general vibration equation as,

                                                       ......(i)

Given,

m = 16 lb

Therefore,

c = 1.5 lb·sec/ft

From (i)

                                     ......(ii)

lets first find complementary function

Finding roots we get

Therefore

Now lets find particular integral

So the total solution becomes

Differentiating with respect to t

The question contains only 2 conditions and we have 4 constants.