Can anyone solve this integral for spring mass oscillation?

In summary, the conversation discusses solving a second order differential equation by direct integration. The equation involves two variables, x and t, which need to be separated in order to integrate both sides. The integral 1/(a-b*x^2)^(1/2) can be solved using a trig substitution or an integral table.
  • #1
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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  • #2
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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  • #3
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?
 

1. What is an integral for spring mass oscillation?

An integral for spring mass oscillation is a mathematical representation of the motion of a mass attached to a spring. It takes into account the displacement, velocity, and acceleration of the mass over time.

2. Why is solving this integral important?

Solving this integral is important because it allows us to accurately predict and understand the behavior of spring mass systems. It is also a fundamental concept in physics and engineering.

3. Is there a specific method for solving this integral?

Yes, there are several methods for solving integrals for spring mass oscillation. Some common approaches include using the power rule, substitution, and integration by parts.

4. Can this integral be solved analytically or numerically?

This integral can be solved using both analytical and numerical methods. Analytical solutions involve finding a closed-form expression for the integral, while numerical solutions use algorithms to estimate the value of the integral.

5. Are there any real-world applications of this integral?

Yes, this integral has many real-world applications, including predicting the behavior of springs and pendulums, analyzing the motion of vehicles on suspension systems, and understanding the behavior of elastic materials.

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