A surgical microscope weighing 200 lb is hung from a ceiling by four springs with stiffness 25 lb/ft. The ceiling has a vibration amplitude of 0.05mm at 2 Hz (a typical resonant frequency of a building). a) If there is no damping, how much transmitted vibration (amplitude of displacement) does the microscope experience

If there is no damping, the amount of transmitted vibration that the microscope experienced is   =

Explanation:

The motion of the ceiling is y = Y sinωt

y = 0.05 sin (2 π × 2) t

y = 0.05 sin 4 π t

K = 25 lb/ft  × 4  sorings

K = 100 lb/ft

Amplitude of the microscope  

where;

=

= 4.0124

replacing them into the above equation and making X the subject of the formula:

Therefore; If there is no damping, the amount of transmitted vibration that the microscope experienced is   =

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