Mass-Spring Equilibrium Point: Affect on Position, Velocity, & Acceleration

In summary, the conversation discusses the parameters of a damped mass-spring system and how they change when the system is oscillating through its equilibrium position. The third term of the equation is zero at this point and the acceleration is also assumed to be zero, leaving only the second term non-zero. However, there may still be a damping force and thus an acceleration at y = 0. The flaw in the reasoning is assuming that the first term will also be zero.
  • #1
The Head
144
2
Somehow I have become confused about the different parameters of a damped mass-spring system that follows:

my'' + cy' + ky = 0

When the mass-spring system is oscillating, but passing through its equilibrium position (y=0), the third term will be zero. And from the best I can rationalize, the acceleration is also zero at this point and the velocity is maximal. Thus the first term is zero and the second non-zero. So I am left with one non-zero term equal to zero.

Where is the flaw in my reasoning? Thanks.
 
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  • #2
The Head said:
When the mass-spring system is oscillating, but passing through its equilibrium position (y=0), the third term will be zero.
So far, so good.
And from the best I can rationalize, the acceleration is also zero at this point and the velocity is maximal. Thus the first term is zero and the second non-zero. So I am left with one non-zero term equal to zero.
The acceleration y'' will only be zero if both other terms are zero (or add to zero). As long as it's moving, there will be a damping force (second term) and thus an acceleration at y = 0.
 

1. What is a mass-spring equilibrium point?

A mass-spring equilibrium point is a state in which the forces acting on a mass-spring system are balanced, resulting in a stationary position with no net force acting on the mass.

2. How does the mass-spring equilibrium point affect the position of the mass?

The mass-spring equilibrium point determines the position of the mass, as it is the point at which the spring is neither compressed nor stretched, resulting in a stationary position.

3. Does the mass-spring equilibrium point affect the velocity of the mass?

Yes, the mass-spring equilibrium point does affect the velocity of the mass. When the mass is at the equilibrium point, it has zero velocity as there is no net force acting on it. However, as the mass moves away from the equilibrium point, the velocity increases.

4. How does the mass-spring equilibrium point affect the acceleration of the mass?

The acceleration of the mass is affected by the mass-spring equilibrium point as it is the point at which the net force acting on the mass is zero. This means that the mass will not experience any acceleration at the equilibrium point.

5. Can the mass-spring equilibrium point change?

Yes, the mass-spring equilibrium point can change depending on the external forces acting on the system. For example, if an external force is applied to the mass, it will shift the equilibrium point and change the position, velocity, and acceleration of the mass.

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