# Force Transmitted to the support (Vibrations)

Consider the spring mass dashpot system shown below which is acted upon by a harmonic excitation force F(t). The reference is taken at the equilibrium position of the system when no F(t) was present. At time t=0, F(t) acts and displaces the system from its equilibrium.

I'm interested in knowing the force transmitted to the support. I proceeded in the following manner: At time t, the spring would be stretched by $$x-x_0$$ and the end of damper will have a velocity equal to x(dot on the top)

The resulting expression I get for transmitted force has an mg in it. However all the sources I'm referring to state the expression with no mg. Where am I wrong in the analysis?

• could you provide which expressions you are referring to? (It seems as though you are trying to obtain the transmissibility ratio.)
– NMech
Sep 30, 2021 at 4:45
• Yes, eventually the transmissibility ratio, but prior to that - the force transmitted to the support as a function of time. Sep 30, 2021 at 5:27
• there can be many reasons for that ( I still don't know your other references). However, I think is that the vibration will be largely unaffected by the gravity. Gravitational forces are a constant term that will be added to the mean value. The transmissability ratio offers a relationship between the excitation force (not gravity) and the transmitted force.
– NMech
Sep 30, 2021 at 5:34
• Ohh. Here is a screenshot from the textbook I'm referring to (with highlighted equation I'm talking about) - drive.google.com/file/d/1-Cg3qAYTk4niUEnZldXzO8Hm-1FoLw4w/… Sep 30, 2021 at 5:42
• That looks like rao's mechanical vibration's right?
– NMech
Sep 30, 2021 at 5:46