Differentials

Question 1

How do you find the integrating factor?

Answer 1

R= e^ integral of p(x)

Question 2

What is the complimentary function when the root is complex

Answer 2

Y= e^Dx ( AcosEx + BsinEx)

Question 3

Formula of simple harmonic motion
Including r alpha and period

Answer 3

D^2x/ dt^2 + w^2 x^2 = 0

R sin ( wt + a) where r is the amplitude and a is the phase shift and the period is 2pi/ w

Question 4

When is there heavy dampening?

Answer 4

Discriminant > 0, x= Ae^mt + B e^ m2t

Question 5

When is there critical dampening

Answer 5

Discriminant = 0, x= e^mt ( A + Bt)

Question 6

When is there light dampening

Answer 6

Discriminant < 0,
x= e^pt ( Acosqt + Bsinqt)