## Sunday, June 12, 2016

### EJSS Mass Scale Model

updated
 http://iwant2study.org/ospsg/index.php/interactive-resources/physics/01-measurements/7-shmmassscale

EJSS Mass Scale Model an orginal model by lookang
updated 08 july 2015

 1.00 kg scale photo by rachelle lee
version 1.00 kg

 4.00 kg scale photo by rachelle lee
version 4.00 kg

 5.0 kg scale photo by rachelle lee
version 5.0 kg

## Model:

The equations that model the motion of the mass scale system are:

Mathematically, the restoring force $F$ is given by

$F = - k (\theta - \theta_{0})$

where $F$ is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and $\theta$ is the displacement from the equilibrium position $\theta_{0}$ (in radians).

Thus, this model assumes the following ordinary differential equations:

$\frac{\delta \theta }{\delta t} = \omega$

$\frac{\delta \omega }{\delta t} = -\frac{k}{m} (\theta - \theta_{0}) - b\frac{\omega}{m}$

where the terms

$-\frac{k}{m} (\theta - \theta_{0})$ represents the restoring force component as a result of the coil spring extending and compressing.

$- b\frac{\omega}{m}$ represents the damping force component as a result of dampers retarding the  mass's motion.

## Rotation:

in order of the rotation to be sync with the typically mass scale

transformation of $\frac{\pi}{2}$ is made for the arrows so that it starts at the top
initial angular displacement of  $2 \pi$ so that the pointer moves towards final angle of random value say $\pi$ which is 2.50 kg.