Problem 1.37
[Difficulty: 1]
Given:
Equation for vibrations.
Find:
Dimensions of c, k and f for a dimensionally consistent equation. Also, suitable units in SI and BG systems.
Solution:
Use the vibration equation to find the diemsions of each quantity
The first term of the equation is
m
d
2
x
dt
2
⋅
The dimensions of this are
M
L
t
2
×
Each of the other terms must also have these dimensions.
Hence
c
dx
dt
⋅
ML
⋅
t
2
=
so
c
L
t
×
⋅
t
2
=
and
c
M
t
=
kx
⋅
⋅
t
2
=
so
kL
×
⋅
t
2
=
and
k
M
t
2
=
f
⋅
t
2
=
Suitable units for c, k, and f are
c:
kg
s
slug
s
k:
kg
s
2
slug
s
2
f:
kg m
⋅
s
2
slug ft
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 Fall '07
 Lear
 Fluid Mechanics, Force, Mass, 2 m, suitable units, dimensionally consistent equation, 2 2 kg

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