Calculating the period of a harmonic function

Click For Summary

Discussion Overview

The discussion focuses on calculating the period of harmonic functions, specifically examining the cosine function and its parameters. Participants explore the implications of phase constants and the combination of sine and cosine functions in determining periods, with an emphasis on both analytical and graphical methods.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant presents the function x=16cos(10t+5π/3) and asks how to calculate its period for graphing purposes.
  • Another participant notes that the cosine function repeats when 10t is increased by 2π, suggesting this as a basis for calculating the period.
  • A participant references the general formula T=2π/a for the period of a cosine function and questions whether the phase constant (5π/3) affects this calculation.
  • It is stated that the period remains T=2π/10, indicating that the phase constant does not influence the frequency or period.
  • A new question is raised regarding the period of a function combining sine and cosine, specifically x(t)=4sin(15t)-3cos(9t+1.1), with a participant noting a discrepancy between an analytical approach and a graphical result obtained from MATLAB.

Areas of Agreement / Disagreement

Participants generally agree that the phase constant does not affect the period of the cosine function. However, the discussion regarding the period of a combined sine and cosine function remains unresolved, with differing methods of analysis presented.

Contextual Notes

There is uncertainty regarding the analytical calculation of the period for functions that combine sine and cosine, as well as potential dependencies on specific definitions or methods used in analysis.

No0bzDown
Messages
3
Reaction score
0
For a example, x=16cos(10t+5π/3) ,S.I.

How am i supposed to calculate the period?(in order to do the graph)


Thanks in advance
 
Mathematics news on Phys.org
You cos function repeats when 10t increased by [itex]2 \pi[/itex]. See if you can work it out based on that.
 
If we have something like this: f(x) = cos(at)

then T= 2π/a

But i really want to know if on my first example 5π/3 is playing any role on this formula.

I mean if x=16cos(10t + 5π/3)

Is period still T = 2π/a = 2π/10 ?
 
No0bzDown said:
If we have something like this: f(x) = cos(at)

then T= 2π/a

But i really want to know if on my first example 5π/3 is playing any role on this formula.

I mean if x=16cos(10t + 5π/3)

Is period still T = 2π/a = 2π/10 ?

Yes it is. The phase constant (5 Pi /3) does not change the frequency or period.
 
Nice. Thanks very much.
 
What if you have a harmonic function with both cos and sin?

such as: x(t)=4sin(15t)-3cos(9t+1.1)

can you find the period of this analytically? I have found this has a period of 2.1 by plotting it in MATLAB, but can't figure out how to calculate this analytically...
 
Last edited:

Similar threads

High School Can a function have two fundamental periods?
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Please discuss discrete Fourier analysis
  • · Replies 12 ·
Replies
12
Views
2K
High School Arithmetic progression, Geometric progression and Harmonic progression
  • · Replies 5 ·
Replies
5
Views
2K
MHB ACT.trig.01 What is the period of the function csc 4x
  • · Replies 2 ·
Replies
2
Views
2K
MHB Graphing Trig Function: Amplitude 4, Period (2\pi/3), Range [-4,4]
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Dispersion: Why are Sine-like Functions Fundamental?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
High School What function satisfies this table?
  • · Replies 51 ·
2
Replies
51
Views
4K
How to prove that motion is periodic but not simple harmonic?
  • · Replies 51 ·
2
Replies
51
Views
4K
High School Periodic smooth alternating series other than sin and cos
  • · Replies 16 ·
Replies
16
Views
3K