Intro to Simple Harmonic Motion (Horizontal Springs) Video Lessons

Concept

# Problem: 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

###### FREE Expert Solution

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:

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

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###### Problem Details

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