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Dynamic Measurement Quantities

Dynamic Measurement Quantities: Introduction

The Motion is characterized by three quantities: Displacement – Velocity – Acceleration

Displacement: Displacement quantifies the change in spatial position

Velocity: Velocity is the rate of change of displacement with respect to time

Acceleration: Acceleration is the rate of change of velocity with respect to time

Displacement, Velocity and Acceleration Relationships

For sinusoidal motion, displacement, velocity and acceleration are expressed by:

displacement d = d₀ sin [2πft]

velocity v = d₀ (2πf ) cos [2πft]

acceleration a = -d₀ (2πf )² sin [2πft]

where d₀ = displacement amplitude / f = frequency / t = time

Amplitude Relationships and Units

Mathematical relationships between displacement, velocity and acceleration

d =	v/πf	Ga/2(πf)2
v =	πfd	Ga/2 πf
a =	2(πf)²d/g	2 πfv/G

Gravitational units

Normalizes acceleration to gravitational acceleration constant:

g = acceleration/ G

where G is the gravitational acceleration constant in the appropriate units

English Units	SI Units	Metric Unit and Acc in g
d = in peak to peak v = in/s peak a = g peak f = Hz G = 386.09 in/s2 π = 3.1416	d = mm peak to peak v = mm/s peak a = m/s2 peak f = Hz G = 10000 mm/s2 π = 3.1416	d = mm peak to peak v = mm/s peak a = g peak f = Hz G = 9806.6 mm/s2 π = 3.1416