The Sense of Restoring Force in Vibrations

[mech-eng]

I would like to ask about the sense of the restoring force in mechanical vibrations.

Comment 2 says that resultant force is opposite the motion but I have some hesitations about it because let's think the situation that mass is moving back upward to its equilibrium position. In this case the sense of the force is to its equilibrium point and acceleration is also to its equilibrium point. Because when the mass moves downward and when the velocity of mass come to zero because of the spring force, this time mass will start to move in the sense of the spring force.

Would you like to explain it?

Source: Engineering Mechanics by Joseph E. Shelley

Thank you.

 

[Dale]

You are correct. The sense of the force is opposite to the displacement, not opposite to the velocity. I assume that "motion" means velocity, as usual.

 

[Redbelly98]

You are correct. The sense of the force is opposite to the displacement, not opposite to the velocity. I assume that "motion" means velocity, as usual.

Agreed. This is poorly worded, IMHO, on the part of the author.

The phrase (also in Comment 2) that a negative acceleration means a decreasing velocity, therefore the mass is slowing down, is just wrong. If the velocity happens to be negative, a negative acceleration would mean the mass is speeding up. (The phrase "decreasing velocity" seems ambiguous: does it mean a decreasing magnitude, or a change toward more negative values? The author seems to have confused these two meanings.)