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**Spring Mass Damping System Question?? Maximum acceleration??**

## Homework Statement

Hello,

I was wondering if anyone knows how to go about answering these type of questions...

Anti-vibration mounts are used to attach an instrument of mass 5kg to a panel. The panel is vibrating with an amplitude of 1mm at a frequency 30Hz.

Determine

a)the stiffness of the mounts which provides an isolation effect, i.e a reduction in the vibration amplitude of the attached instrument...

b)the maximum acceleration to which the instrument is exposed when the mounts have an effective stiffness of 30kN/m and also provide viscous damping with a damping coefficient of 60Ns/m

c)the acceleration amplitude of the instrument at resonance

## Homework Equations

Given MF= X/Y = √( (1 +(2zr)

^{2})/((1-r

^{2}) 2 + (2zr)

^{2}) )

where X- instrument amplitude of vibration

Y- panel amplitude of vibration

r- frequency ratio

z- damping ratio

MF- magnification factor

We have the following equations

Critical Damping Coefficient c

_{c}= 2√km = 2mω

_{n}

Equations

f = ω

_{n}/ 2*(pi)

ω

_{n}= √k/m

c

_{c}= 2√km

z = c/c

_{c}

ω

_{d}= ω

_{n}√(1-z

^{2})

## The Attempt at a Solution

--------------------

Solutions

a) Post 3 for solution

b) Post 4 for solution

c)??

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