This video explains how to determine a linear second order homogeneous differential equation to model free damped motion. Then the IVP is solved to find the displacement function.

# VIII. Differential Equations

# Ex: Determine a Dampening Force For An Overdamped System (Free Damped Vibration)

This video explains how to determine the dampening force with a given velocity to make system overdamped.

# Ex: Determine a Dampening Force For An Critically Damped System (Free Damped Vibration)

This video explains how to determine the dampening force with a given velocity to make system critically damped.

# Ex 1: Write a Step Function Using the Unit Step Function

This video explains how to write an equation of a step function using the unit step function.

# Ex 2: Write a Step Function Using the Unit Step Function

This video explains how to write an equation of a step function using the unit step function.

# Ex: Write a Ramp Function Using the Unit Step Function

This video explains how to write an equation of a ramp function using the unit step function.

# Ex: Find the Laplace Tranform of a f(t) Times a Unit Step Function

This video explains how to determine the Laplace transform of the product of a function of t and a unit step function.

# Ex: Find the Laplace Transform of a Step Function (Method #2)

This video explains how to determine the Laplace transform of a step function.

# Ex: Find the Laplace Transform of a Step Function (Method #1)

This video explains how to determine the Laplace transform of a step function.

# Ex: Find the Laplace Transform of a Piecewise Defined Function (Ramp)

This video explains how to determine the Laplace transform of a piecewise defined function.