how to find period of a function

Aamplitude, Period, Phase Shift and Frequency

Some functions (like Sine and Cosine) repeat forever
and are called Periodic Functions.

The Menstruation goes from one peak to the next (or from any betoken to the next matching point):

The Amplitude is the summit from the center line to the peak (or to the trough). Or nosotros can measure the height from highest to lowest points and divide that by 2.

The Phase Shift is how far the function is shifted horizontally from the usual position.

The Vertical Shift is how far the office is shifted vertically from the usual position.

All Together Now!

We can take all of them in one equation:

y = A sin(B(x + C)) + D

• amplitude is A
• period is iiπ/B
• phase shift is C (positive is to the left)
• vertical shift is D

And hither is how information technology looks on a graph:

Note that we are using radians here, not degrees, and at that place are 2π radians in a full rotation.

Instance: sin(x)

This is the basic unchanged sine formula. A = one, B = 1, C = 0 and D = 0

And so amplitude is one, menstruum is iiπ , there is no phase shift or vertical shift:

Example: 2 sin(four(x − 0.five)) + iii

• amplitude A = two
• flow 2π/B = 2π/4 = π/two
• phase shift = −0.5 (or 0.five to the correct)
• vertical shift D = 3

In words:

• the 2 tells us it volition exist 2 times taller than usual, then Amplitude = 2
• the usual period is 2 π , only in our example that is "sped up" (made shorter) past the 4 in 4x, so Period = π/2
• and the −0.5 means information technology will be shifted to the right by 0.5
• lastly the +iii tells us the center line is y = +3, so Vertical Shift = three

Instead of 10 we can have t (for time) or peradventure other variables:

Example: three sin(100t + ane)

First we need brackets around the (t+1), and so we tin can start by dividing the 1 by 100:

iii sin(100t + ane) = 3 sin(100(t + 0.01))

Now we tin see:

• aamplitude is A = 3
• period is 2π/100 = 0.02 π
• phase shift is C = 0.01 (to the left)
• vertical shift is D = 0

And we get:

Frequency

Frequency is how often something happens per unit of time (per "i").

Instance: Here the sine function repeats 4 times between 0 and ane:

So the Frequency is 4

And the Period is ane 4

In fact the Menstruation and Frequency are related:

Frequency = 1 Period

Period = 1 Frequency

Example from before: 3 sin(100(t + 0.01))

The period is 0.02 π

Then the Frequency is 1 0.02π = 50 π

Some more than examples:

Period	Frequency
1 10	10
1 4	4
1	1
5	1 5
100	1 100

When frequency is per second it is called "Hertz".

Instance: fifty Hertz means 50 times per second

The faster it bounces the more than it "Hertz"!

Animation

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Source: https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html

Posted by: fieldsforomed.blogspot.com

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