Modeling Deflection of Attached Plate in Sinusoidal Motion

[Mech-Master]

Hello everyone,

Assume that you have a flat plate, that is moving up and down in a sinusoidal motion with the following equation:

y = yo*sin(2*pi*f*t)

where yo is the amplitude of the motion, f is the frequency and t is time.

There is another smaller size plate attached to the edge of the larger one. The two plates are connected by a spring rod at the hinge.

When the larger plate oscillates with the above equation, the smaller plate starts to deflect.

I would like model the angle of this deflection as a function of time. The angle is measured relative to the flat pate.

I've already determined the torsion constant and hence the natural frequency of the spring. But I'm really not sure how to proceed after that.

Any help will be really appreciated.

 

[elegysix]

It sounds to me like there are 3 forces here. The driving force on the smaller plate, the force due to gravity, and the force due to the spring. Have you tried to write out a DE with those?

Note: I suspect the spring may have to be sufficiently stiff for a closed form solution to exist.