# Max Spring Force in SHM: Where & Why?

• Buddhapus17
In summary, the question is asking where the magnitude of the force from the spring on the mass is maximum in an oscillating system. The answer is at the negative amplitude, where the spring is stretched the most. This is because the only two forces acting on the mass, the spring force and the weight force, are in opposite directions at this point. There is no symmetry between the top and bottom of the oscillation, as gravity also plays a role in the net restoring force.
Buddhapus17

## Homework Statement

Answer the following question for a mass that is hanging on a spring and oscillating up and down with simple harmonic motion.

## Homework Equations

Where in the motion is the magnitude of the force from the spring on the mass a maximum?

## The Attempt at a Solution

I drew two free body diagrams for the oscillating mass: one at the positive amplitude, and one at the negative amplitude. At the positive amplitude, the spring force and the weight force, the only two forces acting on the mass, are pointed downward. At the negative amplitude, the spring force is in the positive direction (up the y-axis) and the weight force is in the negative direction. I believe the answer to this question is that the spring force will be maxed at the negative amplitude. I don't quite understand that. Since we're talking about magnitudes, shouldn't the spring forces be equal at the top and bottom of the oscillation? Isn't there some kind of symmetry?

All help is appreciated.

Where is the displacement maximum?

Buddhapus17 said:
I believe the answer to this question is that the spring force will be maxed at the negative amplitude.
Of course. That's where the spring is stretched the most.

I don't quite understand that. Since we're talking about magnitudes, shouldn't the spring forces be equal at the top and bottom of the oscillation? Isn't there some kind of symmetry?
Don't confuse the spring force with the net restoring force. There's also gravity to consider.

## 1. What is the maximum spring force in SHM?

The maximum spring force in SHM refers to the point in a simple harmonic motion where the spring is stretched or compressed to its maximum limit. This is also known as the point of maximum displacement from the equilibrium position.

## 2. Where does the maximum spring force occur in SHM?

The maximum spring force occurs at the extreme points of the motion, where the displacement is maximum. This can be at either the positive or negative maximum displacement from the equilibrium position.

## 3. Why does the maximum spring force occur in SHM?

The maximum spring force occurs because of the properties of a spring. In SHM, the spring is stretched or compressed due to the restoring force acting on it. At the maximum displacement, the restoring force is at its maximum, resulting in the maximum spring force.

## 4. How is the maximum spring force related to the amplitude in SHM?

The maximum spring force is directly proportional to the amplitude in SHM. This means that as the amplitude increases, the maximum spring force also increases. This relationship can be represented by the equation F = -kA, where F is the maximum spring force, k is the spring constant, and A is the amplitude.

## 5. Can the maximum spring force be greater than the restoring force in SHM?

No, the maximum spring force cannot be greater than the restoring force in SHM. The restoring force is the force that brings the system back to its equilibrium position, and it is always equal and opposite to the maximum spring force at any point in the motion. This ensures that the system remains in equilibrium and the motion remains periodic.

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