Converting Linear Equation to Angular Equation

In summary, the conversation is about converting a linear equation with variables x'' and x' to angular terms. The equation is transformed using the small angles approximation and the spring constant is changed to ω^2*m. The final equation is IΘ'' + (g/L)Θ' + ω^2IΘ = 0.
  • #1
mpm
82
0
Can anyone help me convert this linear equation to angular terms?

mx'' + f*sin(x') + kx = 0

x'' = x double dot
x' = x dot

Im having trouble find info on changing this.
 
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  • #2
Well so far I have:

IΘ'' + (g/L)Θ' + ? = 0

I used the small angles approximation which got rid of the sin(Θ').

Can anyone help me turn the kx itno angular terms?
I know x goes to Θ but not sure about the spring constant.
 
  • #3
I just found something.

Im thinking k = ω^2*m

So that makes this ω^2*m*Θ

and m = I

so my final equation is

IΘ'' + (g/L)Θ' + ω^2IΘ = 0

Does this look right?
 

1. What is a linear equation and an angular equation?

A linear equation is an algebraic equation that represents a straight line on a graph. It has the form y = mx + b, where m is the slope and b is the y-intercept. An angular equation, also known as a trigonometric equation, involves trigonometric functions such as sine, cosine, and tangent.

2. Why would I need to convert a linear equation to an angular equation?

Converting a linear equation to an angular equation can be useful when working with angles and trigonometric functions. It allows you to solve problems involving angles and can help you find missing information, such as side lengths or angles in a triangle.

3. What is the process for converting a linear equation to an angular equation?

The process for converting a linear equation to an angular equation involves substituting the x-values in the linear equation with corresponding trigonometric functions, such as sine, cosine, or tangent. This will create an equation with angles instead of x-values.

4. Can any linear equation be converted to an angular equation?

No, not all linear equations can be converted to angular equations. The equation must contain one or more variables that can be represented by trigonometric functions. For example, an equation such as y = 3x + 5 cannot be converted, but an equation such as y = 3sinx + 5 can be converted.

5. Are there any limitations or restrictions to converting a linear equation to an angular equation?

Yes, there are a few limitations and restrictions when converting a linear equation to an angular equation. The equation must be in the form y = mx + b, and it must contain at least one variable that can be represented by a trigonometric function. Additionally, the equation must be solvable using trigonometric identities and laws.

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