Find Why K is Always Bigger than 1 for e^-t/k * sin2t

  • Thread starter Procrastinate
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In summary, the function e^{\frac{-t}{k}}\sin2t is restricted to k>1 and a dot should not be next to t. While values like 0.9 and 0.8 can be graphed, zero yields a math error. This may be related to harmonic motion, but further exploration is needed to determine the physical reason for this restriction.
  • #1
Procrastinate
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I have a function that states:

[tex]e^{\frac{-t}{k}}\sin2t[/tex].

With the restriction k>1. There shouldn't be a dot next to the t.

I am meant to figure out why k is always bigger than one but so far, I am hatting a brick wall. Obviously, zero doesn't work because it yields a math error but the other decimals such as 0.9 or 0.8 can be graphed perfectly.

Could someone please give me any hints? I am thinking it might have something to do with time now but I am still blank.
 
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  • #2
You can graph them, but maybe there is some other reason why k is restricted to > 1? Maybe a physical reason? What is the context?
 
  • #3
It's related to harmonic motion (that is the actual context). I was thinking that perhaps it has something to do with a physical aspect. However, the harmonic motion equation (simple) is slightly different to this, so I didn't really pursue the idea further.
 

FAQ: Find Why K is Always Bigger than 1 for e^-t/k * sin2t

Why is K always bigger than 1 in the equation e^-t/k * sin2t?

The value of K in this equation represents the rate of change for the exponential function. In order for the exponential function to decrease at a steady rate, K must be greater than 1. If K were less than 1, the exponential function would decrease at a slower rate, resulting in a smaller value for the entire equation.

What does the e^-t/k term represent in the equation?

The e^-t/k term represents the exponential function, which is a mathematical function that increases or decreases at a steady rate. In this equation, it is used to decrease the overall value of the equation at a constant rate.

3. How does the value of K affect the graph of e^-t/k * sin2t?

The value of K affects the steepness of the graph of e^-t/k * sin2t. A larger value of K will result in a steeper decrease in the exponential function, leading to a sharper peak in the graph. A smaller value of K will result in a more gradual decrease, leading to a smoother peak in the graph.

4. Can the value of K ever be less than 1 in this equation?

No, the value of K must be greater than 1 in this equation in order for it to have a meaningful solution. If K were less than 1, the exponential function would continue to decrease infinitely, resulting in an undefined solution.

5. How is the value of K determined in this equation?

The value of K is typically determined through experimentation or by solving for it in a larger problem. In some cases, the value of K may be given or known based on the context of the problem.

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