MHB Finding Functions: Amplitude, Period, Frequency, Phase Angle

  • Thread starter Thread starter fordy2707
  • Start date Start date
  • Tags Tags
    Functions
AI Thread Summary
The discussion focuses on determining the amplitude, period, angular frequency, and phase angle of the function y=3cos(4t+π/2). The amplitude is confirmed as 3 units, while the period is calculated to be π/2 seconds. The angular frequency is established at 4 radians per second, and the phase shift is identified as -π/8 radians leading. A correction is suggested to describe amplitude in general terms rather than as "amps," which is specific to electrical current. Overall, the calculations and understanding of the function's characteristics are affirmed.
fordy2707
Messages
24
Reaction score
0
hi all can you browse over this please, to see if I've got this correct as I just want to make sure I am getting it.

for the following functions of time,find the amplitude,period ,angular frequency and phase (im assuming it means phase angle there ?)

y=3cos (4t+$\frac{\pi}{2}$)

amplitude =3 Amps

time period =$\frac{2\pi}{4}$ =1.57 seconds

angular frequency =$\frac{2\pi}{1.57}$ =4 radians per seconds

phase angle =$\frac{\pi}{2}$ radians leading
 
Mathematics news on Phys.org
What I would do is first write the function in the form:

$$y=A\cos\left(B(t-C)\right)$$

In this form, we can find directly:

Amplitude (in units): $$|A|$$

Period (in time units): $$\frac{2\pi}{B}$$

Angular frequency (in radians per unit of time): $$B$$

Phase Shift (in time units): $$C$$

So, taking the given function, and putting it into this form, we have:

$$y=3\cos\left(4\left(t-\left(-\frac{\pi}{8}\right)\right)\right)$$

What do you find now?
 
so I've done a bit more of my research on phase shift and I see where you got

$-\frac{\pi}{8}$

from ,which am I correct in saying is -C/B =

$\frac{-\frac{\pi}{2}}{4}$

y=3cos (4t+$\frac{\pi}{2}$)

amplitude =3 Amps

time period =$\frac{2\pi}{4}$ = $\frac{\pi}{2}$ seconds

angular frequency =$\frac{2\pi}{1.57}$ =4 radians per seconds

phase shift now being=$-\frac{\pi}{8}$ leading

is this now correct ?
 
The only change I would make is to describe the amplitude as 3 units...amps is a unit of electrical current. :)
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top