LAB #4 report. MAE 106. UCI. Winter 2005
Nasser Abbasi, LAB time: Thursday 2/3/2005 6 PM
Using Newton's law , then we get, when the origin of the coordinates systems is taken as the center of the mass, and taking the upwards motions and forces as positive and downwards forces as negative
Where is the weight of the mass. This is the force that causes the mass to be displaced from its initial position. Let me call this force as (which is constant in this case)
When we take the origin of the coordinates system as the inertial reference of frame, whose origin is distant from the center of the mass, then we get
where
Hence the equation of motion becomes
Apply Laplace transform to the above ODE, we get
So, to find the transfer function between and , set we get
For the 0.2 g nominal range, the specification sheet says that the natural frequency Hz and
Hence since then
and