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

[fordy2707]

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

 

[MarkFL]

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?

 

[fordy2707]

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 ?

 

[MarkFL]

The only change I would make is to describe the amplitude as 3 units...amps is a unit of electrical current. :)