Periodic functions + phase

Question 1

What is a mathematical function?

Answer 1

Concept of a function that describes how one quantity (input) determines the value of another (output)

y= f(x)

Question 2

What is periodic function?

Answer 2

If the output has the same value for input

A function whose graph repeats itself identically from left to right

f(x) = f(x+np)

Question 3

What is period of function?

Answer 3

Horizontal distance required for a complete cycle

Question 4

What are the importance of sinusoids?

Answer 4

1. Data analysis
2. Behaviour of electromagnetic wave
3. Origin of MR signal

Question 5

What is the period of a basic sine and cosine function?

Answer 5

2π

Question 6

what are sinusoids used to describe?

Answer 6

Wheels

Question 7

What indicates the hole of the wheel?

Answer 7

cos(0) + sin (0)

Question 8

What happens when you rotate the wheel?

Answer 8

X axis remains the same, theta will increase

Question 9

What is the ouput of the wheel?

Answer 9

Angle

Question 10

What is input of the wheel?

Answer 10

Time

Question 11

What is period?

Answer 11

Time for one oscillation cycle

Question 12

What is related to the period?

Answer 12

1. Angular frequency

2. Frequency

Question 13

Higher value of angular frequency

Answer 13

The faster the vector is rotating

Question 14

What is the period Ta of the function sin(ωat) ?

Answer 14

how long the rotating vector a takes to do a single revolution

Question 15

What is frequency (fa) of function?

Answer 15

How many times it rotates per second

Question 16

What is phase difference?

Answer 16

Oa-Ob

Oa= Wat
Ob= Wb[t-t1]

Wat-Wb[t-t1]

Question 17

What does one full cycle correspond to?

Answer 17

2π radians

Question 18

What can be expressed as a sinusoidal function?

Answer 18

The magnitude of a rotating vector

Describes bulk magnetisation of precessing magnetic moments in MR physics

Question 19

What can be described with a cosine function?

Answer 19

X coordinates of rotating vector