## Motion: SHM and Wave

Reference: Wave Motion

For constant acceleration with no initial displacement

x = displacement
t = time
v = velocity (change in velocity comes from force)
a = constant acceleration (acceleration relates to force)
v0 = initial velocity

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Rotational Motion

θ = angular displacement
ω = angular velocity
α = constant angular acceleration

T = Period for one complete rotation
ω = angular velocity

f = frequency of motion per unit time

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Simple Harmonic Motion

x = displacement
t = time
v = velocity (change in velocity comes from force)
a = constant acceleration (acceleration relates to force)
ω = angular velocity
A = Amplitude of motion

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Wave Motion

For transverse waves in a cord

vp = velocity of propagation of the pulse in the cord: m/s
S = tension in the cord (intermolecular forces): N
μ = mass per unit length: Kg/m

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For longitudinal waves in a solid

Y = Youngs modulus: N/m2
ρ = density: M/m3

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For longitudinal waves in a fluid

B = Bulk Modulus: N/m2

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For a traveling wave
(Assume θ0 = 3π/2)

yx(t) = the vertical position of the cord at a definite horizontal position, x.
k = the propagation constant (ω/vp)

λ = wavelength

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Energy and Power for a Wave traveling in a Cord

ε = energy per unit length
μ = mass per unit length: Kg/m