Alvl P2: SHM (ch11) Cheat Sheet (DRAFT) by MostAncientDream

condit­ions:
- force/­acc­ele­ration is propor­tional to and in the opposite direction to the displa­cement

a = w²x

> amplitude: max displa­cement from equili­brium
a max = w²A

> displa­cement at any point:
x = Acos(2­pi.ft) (rads)

> velocity at any point:
v = +- 2pi.f(A²-x²)^1/2
v max = 2pi.fA = wA (at equili­brium)

when frequency of external driving force F matches natural frequency

it is 90' out of phase with each other


free vibrations- frequency a system tends to vibrate at in a vibration is called the natural frequency

forced vibrations- a driving force causes systems to vibrate at a different frequency

when external force opposes motion­/op­posite direction of v

- this occurs when energy is transf­erred out of the system adn the total energy is no longer being constant

main types of damping:
1. light dampening where the oscill­ations are damped slowly eg. air resist­anc­e/f­riction
2. heavy damping where the oscill­ations still continue but are brought to a stop more quickly
3. critical damping involves stopping oscill­ations in the quickest time possible
4. overda­mping caused when the force is too great and stops the oscila­tions but takes longer to return to equili­brium position

when frequency of external driving force F matches natural frequency

it is 90' out of phase with each other


free vibrations- frequency a system tends to vibrate at in a vibration is called the natural frequency

forced vibrations- a driving force causes systems to vibrate at a different frequency