Differential Equations and Motion

This video tutorial explains free undamped motion using linear second-order homogeneous differential equations. It covers the setup of a problem involving a weight attached to a spring, calculates the mass and spring constant, and solves the differential equation to find the motion equation. The tutorial also discusses the general and particular solutions, concluding with a graph of the motion.

What type of differential equations are used to describe free undamped motion?

• Non-linear second order

• Non-linear first order

• Linear second order

• Linear first order

In the problem setup, what is the weight of the object attached to the spring?

• 48 lb

• 36 lb

• 12 lb

• 24 lb

What is the initial velocity of the weight when it is released?

• 3 ft/s

• 1 ft/s

• 2 ft/s

• 0 ft/s

How is the mass of the object calculated using the given weight?

• Weight plus gravity

• Weight divided by gravity

• Weight minus gravity

• Weight multiplied by gravity

What law is used to find the spring constant in this problem?

• Boyle's Law

• Ohm's Law

• Hooke's Law

• Newton's Law

What type of roots does the characteristic equation have in this example?

• Imaginary

• Complex

• Real and repeated

• Real and distinct

What is the general form of the solution for the differential equation in this example?

• C1 t^2 + C2 t

• C1 cos(omega t) + C2 sin(omega t)

• C1 ln(t) + C2

• C1 e^(alpha t) + C2 e^(beta t)

What is the value of C1 in the particular solution?

• -1/4

• 1/4

• 1/2

• -1/2

What is the value of C2 in the particular solution?

• 0

• 2

• 1

• -1

What is the final form of the equation of motion?

• X(t) = 4 cos(omega t)

• X(t) = 4 sin(omega t)

• X(t) = -4 sin(omega t)

• X(t) = -4 cos(omega t)