What Is the Time Between Beats for This Displacement Function?

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In summary, the conversation discussed the displacement of a mass as a function and the time between beats. The displacement was given by the equation x = 3cos((10pi)t) + 3cos((11\pi)\t), and the time between beats was determined by finding the period of the envelope function, which is equal to one over the beat frequency. The attempt at solving the problem involved taking the derivative of the function and setting it equal to zero, but no analytical solution was found.
  • #1
BareFootKing
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Homework Statement


The displacement of a mass as a function is given by the equation

x = 3cos((10pi )t) + 3cos((11\pi)\t)

What is the time between beats, i.e the time between occurrence of the maximum displacement?

Homework Equations



At a maximum v = 0

The Attempt at a Solution



I took the derivative of the function and set it equal to zero
10sin((10pi)t) + 11sin((11pi)t) = 0

I can't find an analytical way of solving this problem. I have tried various trig identities , expanding the functions which took an hour but go no where. Is my strategy of finding the zeros this way the right one or should I come up with a different strategy. And if the latter than where should I start from?
 
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  • #2
You want the period of the envelope function.
http://en.wikipedia.org/wiki/Beat_(acoustics )

The time between beats would be one over the beat frequency.
 
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  • #3
Thank you very much for your help.
 

FAQ: What Is the Time Between Beats for This Displacement Function?

What is the concept of finding the time between beats?

The concept of finding the time between beats refers to the process of measuring the duration or interval between two consecutive heartbeats. This can provide important information about heart health and functioning.

Why is it important to find the time between beats?

Finding the time between beats can help identify any irregularities or abnormalities in heart rhythm, which can be indicative of underlying health issues. It can also provide valuable information for monitoring and managing heart conditions.

How is the time between beats measured?

The time between beats is typically measured using an electrocardiogram (ECG or EKG) machine, which records the electrical activity of the heart and displays it as a graph. The time between the peaks on the graph, known as R-R intervals, is used to calculate the time between beats.

What factors can affect the time between beats?

The time between beats can be affected by a variety of factors, including physical activity, emotional stress, medications, caffeine, and alcohol consumption. Health conditions such as heart disease, thyroid problems, and electrolyte imbalances can also impact the time between beats.

What should I do if I notice a significant change in the time between beats?

If you notice a significant change in the time between your heartbeats, it is important to consult a medical professional for further evaluation. They can determine if the change is normal or if it requires further testing and treatment.

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