Explanation on how these solutions can be easily seen

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    Explanation
In summary, the solutions x1(t)=cos(t) and x2(t)=sin(t) can be easily seen by finding their second derivatives and substituting them into the given equation. This will show that both functions satisfy the equation.
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mazz1801
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Explanation on how these solutions can be "easily" seen

Homework Statement



Show that x1(t)=cos(t) and x2(t)=sin(t) are both solutions to the following Equation.

Homework Equations



(d2x/dt2) + x = 0


The Attempt at a Solution



Ok, So I just cannot understand how this can easily be seen! I cannot see it at all!
I know I haven't got any work to show you and that is wrong but I honestly do not know where to start with this.

It is in the middle of some lecture notes and all they say is "this can easily be seen"

Please Help this dummy!:'(
 
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  • #2


Find the second derivatives of sin(t) and cos(t). Once you do that it should be 'easily seen'.
 
  • #3


Gosh now I feel super dumb :P Thanks a million!
 

Related to Explanation on how these solutions can be easily seen

1. How can the solutions be easily seen?

The solutions can be easily seen by using a microscope or other magnifying tool to view them at a higher magnification. This will allow you to see the individual particles that make up the solution and distinguish them from each other.

2. Can the solutions be seen with the naked eye?

Some solutions may be visible to the naked eye, especially if they have a distinct color. However, for a more accurate and detailed view, using a microscope or other magnifying tool is recommended.

3. Are there any specific techniques for viewing solutions?

Yes, there are techniques such as phase contrast microscopy, dark field microscopy, and polarized light microscopy that can enhance the visibility of solutions and provide more information about their composition.

4. Are there any factors that can affect the visibility of solutions?

Yes, factors such as the concentration of the solution, the size and shape of the particles, and the type of microscope used can all affect the visibility of solutions. It is important to carefully consider these factors when trying to view solutions.

5. Can solutions be seen in different states of matter?

Yes, solutions can exist in different states of matter such as solid, liquid, and gas. The visibility of a solution may vary depending on its state, and different techniques may be required to view solutions in different states.

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