Oscillations and Elastic Potential Energy

In summary, the mass of 1.5 kg oscillating on a spring with a spring constant of 145 N/m and an amplitude of 8 cm can be used to find various values such as velocity, acceleration, elastic potential energy, and gravitational potential energy at different points from the equilibrium point. To find the new equilibrium point, the force equation F=-kx is used, where F is equal to the weight of the object. The point chosen to be zero GPE can vary as long as it is consistent. The elastic potential energy can be found by adding or subtracting the additional distances from the new equilibrium point when plugging into the elastic potential energy equation.
  • #1
pewpew23
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Homework Statement



A mass of 1.5 kg oscillates vertically at the end of a lightweight spring. The spring has a spring constant of 145 Newtons per meter. The amplitude of the motion is 8.00 cm. From this data, complete the table below.

I have to find velocity, acceleration, elastic potential energy, etc. at given points from the equilibrium point.
These points are 8 cm, 6cm, 4cm, 2 cm, 0 cm (equilibrium),... -8 cm


Homework Equations



Elastic Potential= 1/2kx^2
KE=1/2mv^2
GPE=mgh

The Attempt at a Solution



Someone told me that the X you plug into 1/2kx^2 is not the distance from equilibrium in the table. They said that you use the formula F=-kx.
In this case, F=mg so mg=-kx
you solve for X, and this becomes your new equilibrium point.
Then you go through and adjust the rest of the distances from equilibrium so that the closest ones to equilibrium (2 cm previously) are now 2 cm away from this new X.
And this new X is the one you plug into 1/2kx^2 to solve for elastic potential.
Is this correct?

And what values would I use for h to solve for GPE?
Using the X (distance from equilibrium) values given in the table would result in some negative GPE...
Do I make the lowest point equal to 0 cm, and adjust the rest to their distance from the lowest point?
 
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  • #2
The nice thing is that you get to choose whichever point you want to be zero GPE. As long as you are consistent you'll get the correct answers. You are right that using the EQ point as zero will give some negative GPE values, but that's okay: that just means that the object is gaining KE and/or Spring PE as it loses GPE. And since the points listed are relative to the EQ point, there's no need to adjust them.

I feel that it really helps to picture this thing bouncing up and down in your head - some of the answers, especially for KE, can come easily this way.
 
  • #3
Okay, so I understand the GPE.

But what about the Elastic Potential?
How do I do that?
Am I supposed to solve for X using mg=-kx?
 
  • #4
That will give you the distance the spring stretched already (because of the mass on it), in other words, the equilibrium position, which you already found. Just add the additional distances to that (or subtract, for the negative ones) when plugging into the SPE equation.
 

FAQ: Oscillations and Elastic Potential Energy

1. What are oscillations and how do they occur?

Oscillations refer to the back and forth movement of an object around its equilibrium position. They occur when there is a restoring force that acts to bring the object back to its equilibrium position after it has been displaced.

2. What is elastic potential energy and how is it related to oscillations?

Elastic potential energy is the potential energy stored in an elastic material when it is stretched or compressed. In the context of oscillations, it is related to the amplitude of the oscillation and the stiffness of the material, as the greater the amplitude and stiffness, the more potential energy is stored.

3. What factors affect the frequency of oscillations?

The frequency of oscillations is affected by the mass of the object, the stiffness of the material, and the amplitude of the oscillation. It is also influenced by external factors such as friction and air resistance.

4. How is the period of an oscillation calculated?

The period of an oscillation is the time it takes for one complete cycle of the oscillation. It can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the stiffness of the material.

5. Can oscillations occur in non-elastic materials?

Yes, oscillations can occur in non-elastic materials as long as there is a restoring force present. For example, pendulums can oscillate even though the material of the string is not elastic. However, the amplitude and frequency of these oscillations may be affected by the material's stiffness.

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