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Adding different Angular frequency w(t)?

Charlie Mack

wrote...

3 years ago

Adding different Angular frequency w(t)?

I am having trouble understanding this. I understand how to solve the equation but can we just add the angular frequency? I thought they have to be the same?

Express in single cosine?

y(t)=5cos(500t+60) + 100cos(100t-30)

Can we just add the 500t and 100t?

The answer is 100.123cos(wt-27.13) ; w=?

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bio_man

wrote...

#1

Educator

3 years ago

Quote from: Charlie Mack (3 years ago)

Can we just add the 500t and 100t?

Unfortunately you cannot.

You can use the following formula:

Set:

$A = 5$

$B = 100$

$\alpha=60$

$\beta=-30$

See if you can get the rest on your own. If not, simply reply back Slight Smile

Slight Smile

See the document below for further reference.

Attached file

Sum_of_Two_Sinusoids.pdf (147.44 KB)

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1 Vote

romir.juwelz

romir.juwelz

wrote...

#2

2 years ago Edited: 2 years ago, romir.juwelz

Was looking long for an answer to this.
Can I somehow use the formulars in your attachement to add a Sine and a Cosine with doubled frequency?

bio_man

wrote...

#3

Educator

2 years ago

Quote from: romir.juwelz (2 years ago)

Was looking long for an answer to this. Can I somehow use the formulars in your attachement to add a Sine and a Cosine with doubled frequency?

Can you show me what the expressions look like?

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