How to find the transfer function (frequency response function) given the EOM

[mattattack900]

for a given spring/damper system the equation of motion is:

[PLAIN]http://img600.imageshack.us/img600/2140/equation1.png

where x is the displacement of a mass from a fixed point
d is a damping constant
L1 and L2 constant lengths
k1 and k2 are 2 spring constants
and Y(t) is a harmonic input fuction

How can i find the transfer function of this system?

 

[GMarsh]

Hi,

You need to find x(t)/y(t). For this you can assume a harmonic forcing function, for example:

Y(t) = Y0 sin(wt)

and corresponding displacement function:

X(t) = X0 sin(wt-phi), where phi is the phase lag between applied force and resultant displacement.

You input these equations in your equation and solve (considering differential xdot and xdotdot). After substitution, replace X0sin(wt-phi) term with x(t).

Then you will get left side of the equation in terms of x(t). x/y gives you FRF.

Being a single dof, it should be easier for you to calculate by hand.

You can refer any standard vibrations book for this.

Best wishes
Geoff