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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/πfGa/2(πf)2
v =πfdGa/2 πf
a =2(πf)²d/g2 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 UnitsSI UnitsMetric 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