## The model

Spring: spring constant k = 19.62 N/m, natural length of spring Lo = 0.650 m, equilibrium length yo = 0.850 m

Load: mass m = 0.400 kg, displacement from equilibrium position y

## Mathematical model:

$ \frac{\delta y}{\delta t} = v_{y} $

$ \frac{\delta v_{y}}{\delta t} = -\frac{k(y_{0}+y)}{m} + g $

## Energies:

kinetic energy (green) $ KE = \frac{1}{2}mv^{2}_{y} $elastic potential energy (red) $ EPE =\frac{1}{2} k (yo+y)^{2} $

gravitational potential energy (blue) $ GPE = m g (L_{o}+y_{o} + y + reference level) $

total potential energy (magenta) $ TPE = EPE + GPE $ elastic and gravitational potential energy,

total energy (black) $ TE = KE + EPE + GPE $ sum of all the energies

## Controls:

The gravitational potential energy is calculated with respect to the reference level (blue horizontal line). This reference level can be adjusted by (1) dragging the blue box at the right end of the reference level or (2) entering the value of the position in the text box at the lower right hand corner.fine < > control buttons for learners to manipulate the model with single incremental precision

Reset button to bring simulation back to original (default)setting.