Superposition of two simple harmonic motion

In summary: In this case, you cannot combine the terms since they have different arguments. The correct answer would be:cos (t+5325) + 1.5 cos (t-5325)In summary, the sum of cos (t+5325) and 1.5 cos (t-5325) cannot be simplified further since they have different arguments. The final answer is cos (t+5325) + 1.5 cos (t-5325).
  • #1
Krokodrile
45
3
Homework Statement
find the sum of cos (t+5325) + 1.5 cos (t+5325)
Relevant Equations
X1 `+ X2
Hey! I am stuck in this problem, i don't know how to sum this ecuations.

I remember that its possible because the direction is the same

So, i try to sum like this:

cos (t+5325)
+
1.5 cos (t+5325)

=1.5 cos (t+5325) I don't know if i fine. I thanks your help, please ;)
 
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  • #2
Krokodrile said:
Homework Statement:: find the sum of cos (t+5325) + 1.5 cos (t+5325)
Relevant Equations:: X1 `+ X2

Hey! I am stuck in this problem, i don't know how to sum this ecuations.

I remember that its possible because the direction is the same

So, i try to sum like this:

cos (t+5325)
+
1.5 cos (t+5325)

=1.5 cos (t+5325) I don't know if i fine. I thanks your help, please ;)
Maybe there is a typo in your post, but otherwise both terms are cos() with the same arguments. So what is 1+1.5?
 
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  • #3
berkeman said:
Maybe there is a typo in your post, but otherwise both terms are cos() with the same arguments. So what is 1+1.5?
oh, yes. I lose my mind for a second.

So, the answer would be:

2.5 cos (t+5325) ?
 
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  • #4
berkeman said:
Maybe there is a typo in your post, but otherwise both terms are cos() with the same arguments. So what is 1+1.5?
And...only a last question: in the case that 5325 have a negative sign like:

cos (t+5325)
+
1.5 cos (t-5325)

=2.5 cos (t) ??

thank you so much for you help
 
  • #5
Krokodrile said:
And...only a last question: in the case that 5325 have a negative sign like:

cos (t+5325)
+
1.5 cos (t-5325)

=2.5 cos (t) ??

thank you so much for you help
No.
 

FAQ: Superposition of two simple harmonic motion

1. What is the definition of superposition of two simple harmonic motion?

The superposition of two simple harmonic motion refers to the phenomenon where two or more waves with the same frequency and amplitude overlap and combine to form a new wave. This new wave has a displacement that is the sum of the individual displacements of the original waves at that point.

2. How is the superposition of two simple harmonic motion represented mathematically?

Mathematically, the superposition of two simple harmonic motion is represented by adding the equations of the individual waves. This results in a new equation with a different amplitude and phase, but the same frequency as the original waves.

3. What is the principle of superposition and how does it apply to simple harmonic motion?

The principle of superposition states that when two or more waves meet at a point, the resulting displacement is equal to the sum of the individual displacements of the waves. This principle applies to simple harmonic motion as the displacement of a wave at a given point is determined by the superposition of multiple waves with the same frequency and amplitude.

4. What are the practical applications of superposition of two simple harmonic motion?

The superposition of two simple harmonic motion has many practical applications, including in the fields of music, optics, and engineering. For example, musical instruments produce sound through the superposition of multiple waves, and lenses use the principle of superposition to form images.

5. How does the superposition of two simple harmonic motion affect the amplitude and frequency of the resulting wave?

The amplitude of the resulting wave from the superposition of two simple harmonic motion is determined by the sum of the amplitudes of the individual waves. The frequency remains the same as the individual waves. However, the phase of the resulting wave may be different from the individual waves, resulting in a different pattern of oscillation.

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