Oscillation Problem -- Why does my way not work?

In summary: The equilibrium point is not the same as the extreme point. In summary, the problem describes a massless spring with a small object attached that is released from a position y and oscillates up and down, with its lowest position being 10cm below y. The frequency of the oscillation is being asked. The correct answer is 2.2 Hertz. The conversation discusses using the equations F=kx, w=sqroot k/m, and f=w/2pi to solve the problem, but there is a conceptual problem with equating the weight and spring force, as the equilibrium point is not the same as the extreme point.
  • #1
katha
3
0
1. Problem Description:
A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest at a position y. The object is then released from y and oscillates up and down, with its lowest position being 10cm below y.
What is the frequency of the oscillation?

Homework Equations


F=kx; w= sqroot k/m ; f= w/2pi ;3. I know that the right answer to the problem is 2.2 Hertz and I know how you could solve it using energy however I was wondering why the following does not give me the right answer. Is my math just wrong or is it a conceptual problem?

My Way:

F=kx
mg = kx ; x= .1m
mg = k (.1)
(9.8 /.1) = k/m
k/m = 98

w = sq-root k/m
w = sq-root (98)
w = 9.89

f = w/(2pi)
f= (9.89)/(2pi)
f= 1.57 Hz

This is obviously not the right answer. I hope you can give me an explanation as to why it's not.
Thanks in advance!
 
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  • #2
katha said:
F=kx
mg = kx ; x= .1m

Why did you equate weight and spring force?
 
  • #3
Mastermind01 said:
Why did you equate weight and spring force?

I don't no if this assumption is true, but I just thought that the mass/spring system's equilibrium point was at .1m and at that point the force of the spring and the force due to gravity should be equal (but in opposite direction).
 
  • #4
katha said:
I don't no if this assumption is true, but I just thought that the mass/spring system's equilibrium point was at .1m and at that point the force of the spring and the force due to gravity should be equal (but in opposite direction).

Do you know the dynamics of oscillation? Think of a pendulum. What happens at its extreme point?
 
  • #5
Mastermind01 said:
Do you know the dynamics of oscillation? Think of a pendulum. What happens at its extreme point?

Ok, I think I see where the problem is. The distance x can't be the equilibrium point because when smth oscillates, it goes beyond its equilibrium point. So F of the spring can't be equal to mg, right?
 
  • #6
katha said:
Ok, I think I see where the problem is. The distance x can't be the equilibrium point because when smth oscillates, it goes beyond its equilibrium point. So F of the spring can't be equal to mg, right?

That is correct.
 

1. Why is my oscillation problem not working?

There could be several reasons why an oscillation problem is not working. It could be due to incorrect initial conditions, an error in the mathematical model, or inappropriate parameter values. It is important to carefully check all the components of the problem to identify the specific cause.

2. How can I fix my oscillation problem?

The solution to fixing an oscillation problem depends on the specific cause. If it is due to incorrect initial conditions, adjusting them to more appropriate values may help. If it is an error in the mathematical model, carefully reviewing and correcting the equations may be necessary. In some cases, changing the parameter values can also help stabilize the system.

3. Can numerical errors cause an oscillation problem?

Yes, numerical errors can lead to an oscillation problem. These errors can arise from limitations in computer precision or rounding errors in calculations. It is important to use appropriate numerical methods and carefully monitor for any potential sources of error.

4. What are some common techniques for solving oscillation problems?

There are several techniques for solving oscillation problems, including stability analysis, parameter optimization, and using control methods. Stability analysis involves examining the behavior of the system over time to determine its stability. Parameter optimization involves adjusting the values of key parameters to find the most appropriate values for stable oscillations. Control methods use feedback to regulate the system and prevent or reduce oscillations.

5. How can I prevent an oscillation problem from occurring?

To prevent an oscillation problem, it is important to have a thorough understanding of the system and its behavior. This includes carefully selecting appropriate initial conditions and parameters, using accurate mathematical models, and implementing appropriate numerical methods. Regularly monitoring the system and making adjustments as necessary can also help prevent or mitigate oscillations.

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