Proof: Show M = B^2 / sqrt(1 - B^2)^2 + 4a^2B^2

[hailtotheking]

Can anyone help with this?

Natural angular frequency ? = ?k/m

Damping Ratio ?= r/(2?km)

Ratio ?= ?/?

Show that M can be expressed as

?^2 / ?(1 - ?^2)^2 + 4?^2?^2

Is just a simple case of substitution?

Cheers

 

[stapel]

Show that M can be expressed as ?^2 / ?(1 - ?^2)^2 + 4?^2?^2

How does "M" relate to "m"?

Note: Since the square of the square root is the absolute value, the expression above can be written as:

. . . . .\(\displaystyle M\,=\,\frac{\beta^2}{\left|1\,-\,\beta^2\right|}\,+\,4\alpha^2\beta^2\)

Eliz.

 

[hailtotheking]

m is the mass of a particle say and M is called the magnification factor.