Can anyone solve this integral for spring mass oscillation?

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Homework Help Overview

The discussion revolves around solving an integral related to spring mass oscillation, specifically focusing on a second equation that involves variables x and t. The original poster expresses uncertainty about directly integrating the equation and mentions a previous attempt to convert it into a second-order differential equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the idea of separating variables in the equation to facilitate integration. The original poster questions how to integrate a specific expression involving a square root in the denominator.

Discussion Status

Some participants have offered guidance on separating variables and suggested methods for integration, including the use of trigonometric substitution. There is an acknowledgment of the complexity of the integral, and the discussion is exploring various approaches without reaching a consensus.

Contextual Notes

The original poster indicates a concern about the appropriateness of their approach to solving the problem, particularly regarding the use of a second-order differential equation. There is also a reference to homework constraints that may limit the methods available for solving the integral.

jin94
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Homework Statement



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So this is the question I need to solve. I was told to directly integrate the bottom equation to solve for x(t). I can solve (1) by differentiating (1) to turn it into 2nd order difffeq (mx''=kx), but I think I'm not allowed to do that ... I have no idea how to solve (2) using direct integration. It looks like a difficult non-linear equation to solve to me. please help me T T

Homework Equations

The Attempt at a Solution


I solved (1) by turning into mx''=kx, but I'm not allowed to do that.
 
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Welcome to PF!

Equation (2) is in terms of the two variables x and t. The ideas is to "separate" the two variables so that just the x variable occurs on one side and the t variable on the other, in such a way that the equation "begs" you to integrate both sides.
 
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TSny said:
Welcome to PF!

Equation (2) is in terms of the two variables x and t. The ideas is to "separate" the two variables so that just the x variable occurs on one side and the t variable on the other, in such a way that the equation "begs" you to integrate both sides.

Thank you! but then how do I integrate 1/(a-b*x^2)^(1/2) dx?
 

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