Solve for x(t), I just keep seeing 0

  • Thread starter lampshade
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For a simple harmonic oscillator, the solution is x(t) = A sin( \omega t + \phi) where A and \phi are constants that you should be able to determine if you use the initial conditions.In summary, the conversation explores the solution to a differential equation involving velocity and position, with the goal of finding the function x(t). There is some uncertainty about the values of E and m, but it is determined that the problem can be approached as a simple harmonic oscillator. The best method is to differentiate the equation and use initial conditions to solve for the function x(t). The final solution is given as x(t) = A sin( \omega t + \phi), where A and \phi can be determined using initial
  • #1
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Homework Statement


[tex]\frac{dx}{dt} = \sqrt{2(\frac{E}{m}) -\omega^2 x^2}[/tex]


Homework Equations



[tex] \frac{dx}{dt} = v [/tex]

The Attempt at a Solution



I keep ending up with the statement x=0.

[tex]\frac{dx}{dt}=\sqrt{2\frac{E}{m} -\omega^2 x^2}[/tex]

Then
[tex](dx/dt)^2 =2\frac{E}{m} -\omega^2 x^2 [/tex]

and 1/2 mv^2 = E

[tex](dx/dt)^2 = v^2 - 2 \omega^2 x^2[/tex]

and with dx/dt being v that makes

[tex]0=\omega^2x^2[/tex]

and then I'm sad :-(
 
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  • #2
lampshade said:

Homework Statement


[tex]\frac{dx}{dt} = \sqrt{2(\frac{E}{m}) -\omega^2 x^2}[/tex]


Homework Equations



[tex] \frac{dx}{dt} = v [/tex]

The Attempt at a Solution



I keep ending up with the statement x=0.

[tex]\frac{dx}{dt}=\sqrt{2\frac{E}{m} -\omega^2 x^2}[/tex]

Then
[tex](dx/dt)^2 =2\frac{E}{m} -\omega^2 x^2 [/tex]

and 1/2 mv^2 = E

[tex](dx/dt)^2 = v^2 - 2 \omega^2 x^2[/tex]

and with dx/dt being v that makes

[tex]0=\omega^2x^2[/tex]

and then I'm sad :-(

What is exactly the question you are trying to answer?

In any case, what is E here? If it's th etotal energy, it's not simply 1/2 mv^2 since there is some potential energy.
 
  • #3
Just find x(t)

I left off a 2 in my work that I just noticed and that seems to have changed things a bit. I have to rework some stuff and maybe see where that ends up. As for what E is, I don't know. Nor do I technically know that m is mass, but it seems awfully like they are. They weren't explicitly defined.
 
Last edited:
  • #4
lampshade said:
Just find x(t)

I left off a 2 in my work that I just noticed and that seems to have changed things a bit. I have to rework some stuff and maybe see where that ends up. As for what E is, I don't know. Nor do I technically know that m is mass, but it seems awfully like they are. They weren't explicitly defined.

Ok, then don't assume E is 1/2 mv^2

This is a simple harmonic oscillator with E = 1/2 mv^2 + 1/2 k x^2.
 
  • #5
If the problem is given just as the differential equation, you don't know what E is nor do you know that m is mass, how do you possibly conclude that E= (1/2)mv2?
(And why is this a physics problem rather than a math problem?)
 
  • #6
HallsofIvy said:
If the problem is given just as the differential equation, you don't know what E is nor do you know that m is mass, how do you possibly conclude that E= (1/2)mv2?
(And why is this a physics problem rather than a math problem?)

At the time I felt that it was more of a physics problem.
 
  • #7
lampshade said:
At the time I felt that it was more of a physics problem.

The best way to attack th eproblem is to differentiate your equation to get the second derivative [tex] \frac{d^2x}{dt^2} [/tex] Use the initial equation to rewrite the first derivative that appears in your result in terms of x itself. Then you will have an equation relating the second derivative to the function x(t) and you will be able to solve.
 

1. What does it mean to "solve for x(t)"?

When we say "solve for x(t)", we are asking for the value of the variable x at a specific time t. This is commonly used in mathematical equations and models to find the value of a variable at a given point in time.

2. Why do I keep getting 0 as the answer when solving for x(t)?

If you keep getting 0 as the answer when solving for x(t), it could mean that the equation or model you are using is incorrect or does not have a solution. It is important to double check your work and make sure all variables and constants are correctly accounted for.

3. Can you provide an example of solving for x(t)?

Sure, let's say we have the equation x(t) = 2t + 5. To solve for x at t=3, we would substitute t=3 into the equation and solve: x(3) = 2(3) + 5 = 11. Therefore, x at t=3 is equal to 11.

4. Is there a specific method for solving for x(t)?

The method for solving for x(t) will depend on the specific equation or model you are using. However, some common methods include substitution, elimination, and graphing. It is important to understand the properties of the equation or model in order to choose the appropriate method.

5. Can we solve for x(t) if there are multiple variables in the equation?

Yes, it is possible to solve for x(t) even if there are multiple variables in the equation. However, this may require using more advanced mathematical techniques such as simultaneous equations or calculus. It is important to fully understand the equation or model before attempting to solve for x(t) in this scenario.

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