How can a conserved quantity test a model?
How can a conserved quantity test a model?
- Record total energy and the initial amplitude.
- Pause near equilibrium and inspect displacement.
- Change mass and explain why total energy stays fixed at fixed k,A.
What to measure
Units and parameter definitions are shown beside every laboratory control and live reading.
The idea underneath
A conservation law is an independent check on a simulated trajectory. In a harmonic oscillator, evaluate kinetic and potential energy at different phases rather than checking only the visual amplitude. Their sum should remain fixed. This model has an analytic solution, so any observed discrepancy beyond floating-point rounding would indicate an implementation or unit error, not a physical dissipation mechanism. Comparing two parameter settings requires accounting for the work done while changing them.
E=½mv²+½kx²=½kA²Units and parameter definitions are shown beside every laboratory control and live reading.
Build the argument
- Write a prediction before running the experiment.
- Hold all but one variable constant, collect repeated measurements, and calculate dimensionless ratios.
- Compare the observations to an analytic limit and document the remaining discrepancy.
Worked example 1
k=12 N/m and A=0.8 m store 3.84 J.
Worked example 2
At x=A/2, one quarter of E is potential and three quarters kinetic.
Applications
A useful model makes a testable prediction and states where it fails. Reproducible settings and exported measurements turn a visual experiment into evidence.
Common misconception
More decimal places do not guarantee greater accuracy. Distinguish discretisation error, uncertainty in inputs, and limits of the physical model.
A further investigation
At a turning point, kinetic energy is…
Check your understanding
At a turning point, kinetic energy is…
- Zero
- All the energy
- Negative
Explanation
Velocity is zero at a turning point.
Model limits
A force changes velocity, not just speed. A massless rod or ideal spring is a model assumption, and small-angle pendulum formulas have a limited range.