Find Frequency of Combined Motion Help

In summary: Hm because the period of the combined motion is the number of cycles it takes for the sine or cosine function to repeat itself. Beats occur because the two functions are not working together in a smooth way.
  • #1
mmmboh
407
0
Find the frequency of the combined motion of:

a)sin(2(pi)t)+cos(13(pi)t-pi/4)
b)sin(3t)-cos[(pi)t]

I know to find the period of the combined motion you do T=n1T1=n2T2 where the n's are integers, so I believe the frequency of the combined motion is just the inverse of the combined period.

For a), I found the period of the sine function to be 1/6, and the period of the cosine function to be 2/13, so T=12(1/6)=13(2/13)=2s, so the frequency is 1/2 Hz...but the answer is actually 6.25 hz.

For b) I found the period of the sin function to be (2/3)pi, and that of the cosine function to be 2, so n1(2/3)pi=n22 has no integer solutions, so there is no determined combined period and thus no determined combined frequency either...but the answer is 0.49 Hz...

Can someone help me please? I already successfully did one of them, but I can't get these..

Also, does it make a difference whether the functions are being added or subtracted?
 
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  • #2
Help please...
 
  • #3
It does not matter if the functions are added or subtracted.

If T1, T2 are the periods, the following condition has to be hold for the new period: T=n1*T1=n2*T2, where n1 and n2 are relative primes.

In case a, T1 = 1, T2= 2/13, so n2=13, n1=2 and T=2, f=0.5

In case b, such integers can not be found as one of the periods is irrational. If it were sin(3(pi)t) -cos((pi)*t), then

T1=2/3 and T2=2 ---> T = 3T1=1T2 = 2, f =0.5

I attach a picture that I think helps to see the period of the new signal.

ehild
 
Last edited:
  • #4
Hm so that means I am right, and the answers at the end of the book are wrong...

Thanks.
 
  • #5
If I use the equation for the "beats" of two combined motions,

[tex]x=2Acos(\frac{\omega_1-\omega_2}{2}t)cos(\frac{\omega_1+\omega_2}{2}t)[/tex]

and I concern myself only with the frequency of the envelope, I get the correct answer for both. Why is this?
 
  • #6
Btw a) should be a)sin(12(pi)t)+cos(13(pi)t-pi/4)
 
  • #7
Beat frequency is not the same as the period of combined motion. You get beats in every case, even when

[tex]
x=2Acos(\frac{\omega_1-\omega_2}{2}t)cos(\frac{\omega_1+\omega_2}{2}t)
[/tex]


is not periodic.

ehild
 
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What is combined motion?

Combined motion is when an object moves in more than one direction at the same time. This can include linear, circular, and oscillating motion.

Why is it important to find the frequency of combined motion?

Knowing the frequency of combined motion can help us understand the behavior and characteristics of the moving object. It can also help us make predictions and calculations for future movement.

How do you calculate the frequency of combined motion?

The frequency of combined motion can be calculated by dividing the total number of cycles by the total time taken. This can also be represented by the formula f = 1/T, where f is frequency and T is the time taken.

What units are used to measure frequency?

The unit used to measure frequency is hertz (Hz). This represents the number of cycles or oscillations per second.

What factors can affect the frequency of combined motion?

The frequency of combined motion can be affected by various factors such as the mass of the object, the force acting on the object, and the medium through which the object is moving. Additionally, any changes in these factors can also affect the frequency.

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