Simple Harmonic Motion

  • Thread starter Calpalned
  • Start date
  • #1
297
6

Homework Statement


My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion".

Homework Equations


The equation of motion ##A \cos (\omega t + \phi)##

The Attempt at a Solution


I know that ##A## stretches the cosine graph vertically, but that the frequency is unaffected. How do ##\omega## and ##\phi## affect the graph?
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,365
1,033

Homework Statement


My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion".

Homework Equations


The equation of motion ##A \cos (\omega t + \phi)##

The Attempt at a Solution


I know that ##A## stretches the cosine graph vertically, but that the frequency is unaffected. How do ##\omega## and ##\phi## affect the graph?
Try some values and see.

or ...

What do you know about shifting and stretching/shrinking of graphs in general?

What is the period of y = cos(x) ?

How does the graph of y = f(x + k) compare with the graph of y = f(x) ?

etc.
 
  • #3
297
6
Try some values and see.

or ...

What do you know about shifting and stretching/shrinking of graphs in general?

What is the period of y = cos(x) ?

How does the graph of y = f(x + k) compare with the graph of y = f(x) ?

etc.
Thank you so much! Is my understanding below valid?

##A## stretches/compresses the graph vertically
##\omega## affects the period. The larger ##\omega## is, the shorter the period.
##\phi## is the horizontal shift and it is negative. That is, a positive value of ##\phi## will shift the graph to the left.
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,365
1,033
Thank you so much! Is my understanding below valid?

##A## stretches/compresses the graph vertically
##\omega## affects the period. The larger ##\omega## is, the shorter the period.
##\phi## is the horizontal shift and it is negative. That is, a positive value of ##\phi## will shift the graph to the left.
Correct.
 

Related Threads on Simple Harmonic Motion

  • Last Post
Replies
17
Views
1K
  • Last Post
Replies
3
Views
849
  • Last Post
Replies
8
Views
143
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
966
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
21
Views
2K
Top