Simple harmonic motion energy conservation problem

In summary, the conversation discusses the maximum kinetic energy of a vertically oscillating mass hanging on a spring. The equilibrium point is a distance d below the relaxed length of the spring and the amplitude of the oscillation is A. The attempt at a solution includes calculating the spring constant and the change in potential energy, but there is another form of potential energy that needs to be considered. The mass is moving vertically and all forces acting on it must be taken into account. With this information, the problem can be solved correctly.
  • #1
al_famky
29
0

Homework Statement


A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?2. Homework Equations

The Attempt at a Solution


I did this:
mg=kd [itex]\rightarrow[/itex] k=[itex]\frac{mg}{d}[/itex]
[itex]\Delta[/itex]E=[itex]\frac{1}{2}[/itex]k[itex](A+d)^{2}[/itex]-[itex]\frac{1}{2}[/itex]k[itex]d^{2}[/itex]=[itex]\frac{1}{2}[/itex][itex]\frac{mg}{d}[/itex]([itex]A^{2}[/itex]+2Ad)
which wasn't the answer, but i don't know where i went wrong.
if anyone could point out the problem, i'd really appreciate your help
 
Last edited:
Physics news on Phys.org
  • #2
There's another form of potential energy that needs to be taken into account.
 
  • #3
TSny said:
There's another form of potential energy that needs to be taken into account.

which is?
 
  • #4
Note that the mass is moving vertically. Think about all of the forces acting on the mass.
 
  • #5
Thank you very much, TSny, for your help, I get it now.
and this question wasn't supposed to have been posted here, sorry for the mix up.
 

Related to Simple harmonic motion energy conservation problem

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. It can be seen in systems such as a mass on a spring or a pendulum.

2. How is energy conserved in simple harmonic motion?

In simple harmonic motion, the total mechanical energy (the sum of kinetic and potential energy) remains constant throughout the motion. This is because the restoring force is conservative and does not dissipate any energy.

3. What is the equation for calculating the energy in a simple harmonic motion system?

The equation for calculating the energy in a simple harmonic motion system is E = 1/2 * k * x^2, where E is the total mechanical energy, k is the spring constant, and x is the displacement from equilibrium.

4. Can simple harmonic motion systems have energy losses?

Yes, simple harmonic motion systems can have energy losses due to external factors such as air resistance or friction. However, in ideal systems, the energy remains constant.

5. How does amplitude affect the energy in a simple harmonic motion system?

The amplitude (maximum displacement) in a simple harmonic motion system does not affect the total energy. However, it does affect the maximum potential and kinetic energy at any given point in the motion.

Similar threads

  • Introductory Physics Homework Help
Replies
16
Views
452
Replies
13
Views
365
  • Introductory Physics Homework Help
Replies
1
Views
905
  • Introductory Physics Homework Help
Replies
13
Views
680
  • Introductory Physics Homework Help
2
Replies
51
Views
2K
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
964
  • Introductory Physics Homework Help
Replies
13
Views
325
Back
Top