What is the potential energy of the spring?

Click For Summary
SUMMARY

The potential energy of a spring can be calculated using the formula U = 1/2 kx², where k is the spring constant and x is the displacement from the equilibrium position. In this discussion, the displacement x was determined to be 0.2 meters using the equation x = A cos(wt), with an amplitude A of 0.33 meters and angular frequency ω of 20.1. The relationship between angular frequency and the spring constant is established by the equation ω² = k/m, which allows for the calculation of k if the mass and ω are known.

PREREQUISITES
  • Understanding of harmonic motion and spring mechanics
  • Familiarity with the equations of motion, specifically x = A cos(wt)
  • Knowledge of angular frequency and its relationship to spring constant
  • Basic algebra for solving equations involving k and x
NEXT STEPS
  • Calculate the spring constant k using the relationship ω² = k/m
  • Explore the implications of varying amplitude on potential energy
  • Learn about energy conservation in harmonic oscillators
  • Investigate the effects of mass on the oscillation frequency of springs
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for practical examples of potential energy in springs.

zachmgilbert
Messages
10
Reaction score
0

Homework Statement


What is the potential energy of the spring?
mass=.52 kg
velocity=-6.54sin(20.1t)
time=40.84 seconds
amplitude=.33 meters
angular frequency=20.1


Homework Equations


U =1/2kx2



The Attempt at a Solution


I used x=Acos(wt) and got .2 meters for x. I know this is right.I don't know how to find k.
 
Physics news on Phys.org


x=Acos(wt)

This solution only satisfies the differential equation m\ddot{x}=-kx if \omega^2 = k/m
 


What is \omega^2?
 


angular frequency squared
 


OK.

If I may ask, what is the independent variable in x=Acos(wt)? I'd like to solve it...
 


Char. Limit said:
OK.

If I may ask, what is the independent variable in x=Acos(wt)? I'd like to solve it...

Hello Char!

The independent variable is time(t) right? The position(x) depends on it.

You now have x,t & k, you should be able to solve for U.
 


Ah, I have the an-word (answer comes from an-swear, meaning "an-word")

I actually wanted to prove the diff e.q. That was mentioned, but I got carried away. The answer is..

Aaaaaaaauuuggh...
Hello Winzer!
 


The Attempt at a Solution


I used x=Acos(wt) and got .2 meters for x. I know this is right.I don't know how to find k.

Then how come the amplitude is 0.33 m?

Anyhow, if you're absolutely sure it's 0.2 m and not 0.33 m, w^2=k/m.
 

Similar threads

Why can we move the spring with constant speed when we apply a force?
  • · Replies 29 ·
Replies
29
Views
3K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Force components for mass attached to two springs
  • · Replies 15 ·
Replies
15
Views
2K
How Is Potential Energy Converted to Kinetic Energy in Physical Systems?
  • · Replies 6 ·
Replies
6
Views
1K
How to find Potential Energy without distance
  • · Replies 4 ·
Replies
4
Views
3K
Why is my method for finding the spring constant incorrect?
  • · Replies 17 ·
Replies
17
Views
3K
How can I calculate the potential energy stored in a compressed spring?
  • · Replies 4 ·
Replies
4
Views
2K
Why is the elastic potential energy in position 2 zero?
  • · Replies 6 ·
Replies
6
Views
2K
Calculate this Spring's Potential Energy
  • · Replies 28 ·
Replies
28
Views
3K