What am I doing wrong with finding the complex amplitude?

In summary, to find the complex amplitude for a given displacement and frequency, the equation (displacement) = Acos(phase constant)cos(wt) - Asin(phase constant)sin(wt) can be used. When plugging in the values for time 0, the correct answer for Acos(phase constant) can be obtained. However, when solving for the sin phase constant, it is necessary to convert the frequency (w) to velocity (v) by using the equation v = w/2pi. This will result in the correct answer of .03 + .0175i.
  • #1
skywo1f
6
0

Homework Statement


i got to find the complex amplitude
i know that w = 50Hz
displacement was 30mm at time 0
and -14mm at time 12ms



Homework Equations



(displacement) = Acos(phase constant)cos(wt) - Asin(phase constant)sin(wt)

The Attempt at a Solution


so I've tried plugging things into the expanded wave equation
and just plugging things in for t = 0
which gives me the correct answer Acos(phase constant) = .03 at time 0
but when i try the second time to get the sin phase constant, it gives me .068
but my answer is supposed to be
.03 +.0175 i
what am i doing wrong?
which equation could i use?
any help would be appreciated
 
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  • #2
nvm figured it out
i was using 50 hz as my w
but really its my v
and i had to convert it with v = w/2pi
 

What is the concept of complex amplitude?

The complex amplitude is a mathematical representation used to describe the magnitude and phase of a complex-valued function. It is composed of a real part and an imaginary part, which together determine the amplitude and phase of the function.

Why is finding the complex amplitude important in science?

Finding the complex amplitude is important because many physical phenomena, such as electromagnetic waves and quantum particles, can be described using complex-valued functions. Understanding the complex amplitude allows scientists to accurately model and predict these phenomena.

How is the complex amplitude calculated?

The complex amplitude is calculated by taking the Fourier transform of a function, which converts the function from the time or space domain to the frequency domain. The complex amplitude can then be represented as a complex number with a magnitude and phase.

What is the difference between complex amplitude and complex number?

A complex number is a number with a real part and an imaginary part. The complex amplitude, on the other hand, is a representation of a complex-valued function and includes both magnitude and phase information, making it a more comprehensive description of the function.

How is complex amplitude used in practical applications?

Complex amplitude is used in a variety of practical applications, such as signal processing, image processing, and quantum mechanics. It is also used in fields such as optics, acoustics, and electrical engineering to analyze and manipulate complex signals and systems.

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