Pressure and oscillations

Pressure definition (Force per unit Area)

p=f/a

Pressure at a depth in a fluid

p=density*gh

Buoyant force (Archimedes' Principle)

B=ρf​Vg

Ratio of submerged volume to total volume for a floating objec

V2/V1 = obj dens/fluid dens

Density

P=m/vol

Angular frequency of a mass-spring system

​w=sqrt(k/m)

Relationship between angular frequency and frequency

W=2pi(freq)

Frequency of a mass-spring system

f = 1/2pi * sqrt(k/m)

Period of a pendulum

2pi(sqrt1/g)

Wave speed

V= sqrt t/u

Total mechanical energy of an SHM system (in terms of amplitude)

E = ½ mVmax²

Linear mass density

u=m/L

Maximum velocity in Simple Harmonic Motion (SHM)

Vmax= wA

Maximum acceleration in Simple Harmonic Motion (SHM)

alphamax=w²A

Wave speed, wavelength, and frequency relationship

V=λf

Fundamental frequency of a string fixed at both ends

f1=V/2L

Harmonic frequencies of a string fixed at both ends (n=1,2,3,...)

fn​=nV/2L

Intensity of a spherical wave (e.g., sound intensity)

I=P/4pi*r²

Velocity in SHM as a function of displacement X

​V=sqrt(k/m(A²-X²)

mu (u)

linear mass density

Omega (w)

Angular frequency

Lambda

Wavelength