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 Engineering Formulae
Applied Mechanics - Vibrations

 Netwon's Law Liquid Pressure Moment of Inertia Pascal's Principle Spring Constant Surface Tension Bouncing Capillary Laws of Conservation of Momentum Vibrations Density

Vibrations

1.        Simple Harmonic Motion

where,

T=period of a vibration, s

n=frequency or vibration per unit time, 1/s

2.    Spring Pendulum

where,

T=period, s

M=mass of pendulum

K=spring

3.     Simple Pendulum

where,

l=length of the pendulum

g=acceleration due to gravity

4.     Wavelength

where,

V=total distance traveled in one second

λ=length of one wave

η=number of waves per second

5.      Speed of sound

where,

V=speed of sound at temperature tc˚C, m/s

Vo=speed at 0˚C, m/s

tc=temperature, ˚C.

6.      Beat Notes

N=n2-n1

where,

N=beat frequency, i.e., number of beats per second

N1, n2=frequencies of two sources producing the sound, vibrations/s

7.       Doppler Effect

where,

No=frequency heard by the observer

ns=frequency of the source

V=velocity of sound

Vs=velocity of source

Vo=velocity of the observer

8.      Intensity of sound

where,

E=intensity of sound at any distance d, microwatts/cm2 or decibels

Eo=intensity of sound at unit distance, decibels

9.       Vibrating Strings

where,

V=velocity of sound, m/s

N=frequency or number of waves passing by per second

λ=length of one wave or wavelength

F=tension in a rope or string, N

M=mass of string per unit length, kg/m

L=distance between two consecutive nodes, m

10.       Sound Wave Through Gas

where,

V=wave velocity, cm/s

P=gas pressure, dynes/cm2

ρ=gas density, g/cm3

K=proportionality constant