# Calculate energy of vertical oscillating spring

• Samuelriesterer
In summary, the problem involves an oscillating mass hung from a vertical spring, with the potential energy of the system at equilibrium being zero for both spring and gravity. The gravitational potential energy, spring potential energy, and total potential energy of the system are then calculated at equilibrium, y cm above equilibrium, and y cm below equilibrium, with the assumption that the spring can compress more than y and that F = -kΔx still holds. The relevant equations used are GPE = mgh and SPE = ½ k x^2, with the variables m = mass, k = spring constant, h = amplitude, and x_0 = position of mass at equilibrium.

#### Samuelriesterer

Problem statement:

An oscillating mass is hung from a vertical spring. Take the potential energy of the system when the spring is at the unstretched length to be zero for both spring and gravity. Calculate the gravitational potential energy, spring potential energy, and total potential energy of the system at:

Equilibrium
y cm above equilibrium
y cm below equilibrium

(Assume the spring can compress more than y and that F = -kΔx still holds)

Relative equations:
GPE = mgh
SPE = ½ k x^2

Work so far:

Equilibrium GPE = mgh
Equilibrium SPE = ½kh^2
Equilibrium TE = mgh + ½kh^2

y cm above GPE = mg(h-y)
y cm above SPE = ½k(h-y)
y cm above TE = mg(h-y) + ½k(h-y)

y cm below GPE = mg(h+y)
y cm below SPE = ½k(h+y)
y cm below TE = mg(h+y) + ½k(h+y)

Samuelriesterer said:
Calculate the gravitational potential energy, spring potential energy, and total potential energy
In terms of what? You must be told what variables to express it in terms of, such as mass, spring constant, etc.

I'm afraid that is all the info the problem states. Let's assume m = mass, k = spring constant, h = amplitude, x_0 = position of mass at equilibrium. I was going to ask my instructor more about it at school tomorrow but I wanted to get a jump on the problem by making my own variables.

## 1. What is the formula for calculating the energy of a vertical oscillating spring?

The formula for calculating the energy of a vertical oscillating spring is E = 1/2 * k * A^2, where k is the spring constant and A is the amplitude of the oscillation.

## 2. How does the spring constant affect the energy of the oscillating spring?

The spring constant directly affects the energy of an oscillating spring. A higher spring constant means a stiffer spring, which will result in a higher energy for a given amplitude.

## 3. Can the energy of an oscillating spring be negative?

No, the energy of an oscillating spring cannot be negative. The formula for calculating energy results in a positive value. A negative value would indicate that the spring is absorbing energy rather than storing it.

## 4. How does the amplitude of the oscillation affect the energy of the spring?

The amplitude of the oscillation directly affects the energy of the spring. As the amplitude increases, so does the energy of the spring. This is because a larger amplitude means the spring is moving a greater distance and therefore storing more energy.

## 5. Is the energy of an oscillating spring constant or does it change over time?

The energy of an oscillating spring is not constant and will change over time. This is due to the fact that the amplitude of the oscillation decreases over time as the energy is dissipated through friction and other factors.