In this problem, we are required to solve for the position(s) that half the maximum velocity and maximum acceleration.

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Acceleration:

$\overline{){\mathbf{a}}{\mathbf{=}}\frac{\mathbf{F}}{\mathbf{m}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{x}}_{\mathbf{0}}}{\mathbf{m}}}$

A mass attached to the end of spring is stretched a distance x0 from equilibrium and released. At what distance from equilibrium will it have a) velocity equal to half its maximum velocity, and b) acceleration equal to half its maximum acceleration

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Simple Harmonic Motion (Horizontal Springs) concept. You can view video lessons to learn Intro to Simple Harmonic Motion (Horizontal Springs). Or if you need more Intro to Simple Harmonic Motion (Horizontal Springs) practice, you can also practice Intro to Simple Harmonic Motion (Horizontal Springs) practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Matthews' class at USF.