Velocity as a function of Position in Simple Harmonic Motion

The video tutorial explains how to derive the equation for velocity as a function of position in a horizontal mass spring system. It covers the relationship between kinetic and potential energy, the derivation of the velocity equation, and the graphical representation of velocity as a function of position. The tutorial also explores the connection between the derived equation and the general equation for an ellipse, and how this relates to simple harmonic motion and constant angular velocity.

How does the total mechanical energy of a horizontal mass spring system relate to kinetic and elastic potential energies?

What is the equation for velocity as a function of position in a mass spring system?

Why is it important to consider both positive and negative values for velocity in a mass spring system?

What does the graph of velocity as a function of position look like for a mass spring system?

Describe the relationship between the position of the mass and its velocity when the mass is at maximum displacement from the equilibrium position.

Explain how the equation for velocity in a mass spring system can be rearranged to show the maximum velocity in simple harmonic motion.

How does the concept of angular velocity relate to the motion of a mass spring system?