Period of Y = SIN(X)+SIN(0.5X)

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Tim
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Am I right in thinking this is 2(pi) ?

TIA

Tim
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Tilemachos
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the period of y=sin(x)+sin(0.5x) is 4Pi

<=====tilemachos======>

Ï "Tim" <[email protected]> Ýãñáøå óôï ìÞíõìá news:[email protected]...
[q1]> Am I right in thinking this is 2(pi) ?[/q1]
[q1]>[/q1]
[q1]> TIA[/q1]
[q1]>[/q1]
[q1]> Tim[/q1]
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Stan Brown
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Tim <[email protected]> wrote in uk.education.maths:
[q1]>Am I right in thinking this is 2(pi) ?[/q1]

The period of sin(x) is 2*pi. The period of sin(ax) is 2*pi/a; thus the period of sin(0.5x) is
2*pi/0.5 = 4*pi.

The period of your function is the LCM of 2*pi and 4*pi, which is 4*pi.

(You could also analyze the function as sin(x) + sin(0.5x) 2 sin(0.5x) cos(0.5x) + sin(0.5x)
[sin(0.5x)] [2 cos(0.5x) + 1] which more clearly has a period of 2*pi/0.5 = 4*pi.)

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
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Tim
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thanks guys

"Tim" <[email protected]> wrote in message news:[email protected]...
[q1]> Am I right in thinking this is 2(pi) ?[/q1]
[q1]>[/q1]
[q1]> TIA[/q1]
[q1]>[/q1]
[q1]> Tim[/q1]
0
Tim
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does that mean Y+sin(0.5x) is 4pi?

"Stan Brown" <[email protected]> wrote in message
news:[email protected]...
[q1]> Tim <[email protected]> wrote in uk.education.maths:[/q1]
[q2]> >Am I right in thinking this is 2(pi) ?[/q2]
[q1]>[/q1]
[q1]> The period of sin(x) is 2*pi. The period of sin(ax) is 2*pi/a; thus the period of sin(0.5x) is[/q1]
[q1]> 2*pi/0.5 = 4*pi.[/q1]
[q1]>[/q1]
[q1]> The period of your function is the LCM of 2*pi and 4*pi, which is 4*pi.[/q1]
[q1]>[/q1]
[q1]> (You could also analyze the function as sin(x) + sin(0.5x) 2 sin(0.5x) cos(0.5x) + sin(0.5x)[/q1]
[q1]> [sin(0.5x)] [2 cos(0.5x) + 1] which more clearly has a period of 2*pi/0.5 = 4*pi.)[/q1]
[q1]>[/q1]
[q1]> --[/q1]
[q1]> Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in[/q1]
[q1]> heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The[/q1]
[q1]> waters? What waters? We're in the desert." "I was misinformed."[/q1]
0
Stan Brown
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Tim <[email protected]> wrote in uk.education.maths:
[q1]>"Stan Brown" <[email protected]> wrote in message[/q1]
[q1]>news:[email protected]...[/q1]

[q2]>> The period of sin(x) is 2*pi. The period of sin(ax) is 2*pi/a; thus the period of sin(0.5x) is[/q2]
[q2]>> 2*pi/0.5 = 4*pi.[/q2]

[q1]>does that mean Y+sin(0.5x) is 4pi?[/q1]

[upside-down posting and over-quoting corrected -- please follow Usenet conventions]

I think you are asking whether the _period_ of y = sin(0.5x) is 4*pi. If so, the answer is in the
article you quoted!

--
Stan Brown, Oak Road Systems, Cortland County, New York, USA http://oakroadsystems.com/ "What in
heaven's name brought you to Casablanca?" "My health. I came to Casablanca for the waters." "The
waters? What waters? We're in the desert." "I was misinformed."
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Virgil
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In article <[email protected]>, "Tim" <[email protected]> wrote:

[q1]> thanks guys[/q1]
[q1]>[/q1]
[q1]> "Tim" <[email protected]> wrote in message news:[email protected]...[/q1]
[q2]> > Am I right in thinking this is 2(pi) ?[/q2]
[q2]> >[/q2]
[q2]> > TIA[/q2]
[q2]> >[/q2]
[q2]> > Tim[/q2]
[q2]> >[/q2]
[q2]> >[/q2]
[q1]>[/q1]
[q1]>[/q1]

I believe that the general property required for this problem is:

If a number of periodic functions all have periods which are positive integer multiples of some
fixed positive quantity, then the sum of all of them will have period equal to a positive integer
multiple of that same fixed quantity, and if the periods of the separate functions are all distinct,
the sum has period equal to the largest possible such fixed positive quantity (the greatest common
meansure of the separate periods).
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