# The Sense of Restoring Force in Vibrations

• B
• mech-eng
In summary, the restoring force in mechanical vibrations is opposite to the displacement, not the velocity. The sense of the force is towards the equilibrium point, and acceleration is also towards the equilibrium point when the mass moves back upward. The statement that negative acceleration means a decreasing velocity is incorrect and could be better clarified by the author.
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.

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.

Dale said:
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.)

## 1. What is the sense of restoring force in vibrations?

The sense of restoring force in vibrations refers to the force that acts on a vibrating object, pulling it back towards its equilibrium position. This force is responsible for the periodic motion of the object and plays a crucial role in understanding the behavior of vibrating systems.

## 2. How does the sense of restoring force affect the frequency of vibrations?

The sense of restoring force is directly proportional to the frequency of vibrations. This means that the stronger the restoring force, the higher the frequency of vibrations. This relationship is described by Hooke's law, which states that the force exerted by a spring (or any other elastic object) is directly proportional to the displacement from its equilibrium position.

## 3. Can the sense of restoring force change over time?

Yes, the sense of restoring force can change over time. This can happen due to various factors such as changes in the elasticity of the object, changes in the environment, or changes in the amplitude of vibrations. In some cases, the sense of restoring force may also decrease over time, leading to a decrease in the frequency of vibrations.

## 4. How does the sense of restoring force impact the amplitude of vibrations?

The sense of restoring force has an inverse relationship with the amplitude of vibrations. This means that the stronger the restoring force, the smaller the amplitude of vibrations. This is because a stronger restoring force pulls the object back towards its equilibrium position more quickly, resulting in smaller oscillations.

## 5. Are there different types of restoring forces in vibrations?

Yes, there are different types of restoring forces in vibrations depending on the nature of the vibrating object. For example, in a simple pendulum, the restoring force is provided by gravity, while in a spring-mass system, the restoring force is provided by the spring's elasticity. Other types of restoring forces include tension, compression, and shear forces.

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