Wave Problem - Phase Shift

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Homework Statement


1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.



Homework Equations





The Attempt at a Solution



a) Amplitude = 6 (inspection)
b) Period = (218.75ms + (-31.25ms)) = 250ms
c) ω=2π/T = 2π / 0.250s = 8π rad/sec
d) dφ=2π/dt = -8π/125
e) frequency = ω/2π = 8π/2π = 4Hz
f) deg = 180 φ/2π = 5.76 deg

y(t) = 6cos(8πt - 8π/125)

So i am not sure on my calculation for the phase shift.

Homework Statement





Homework Equations





The Attempt at a Solution

 

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Answers and Replies

  • #2
ehild
Homework Helper
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Homework Statement


1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.



Homework Equations





The Attempt at a Solution



a) Amplitude = 6 (inspection)
b) Period = (218.75ms + (-31.25ms)) = 250ms
c) ω=2π/T = 2π / 0.250s = 8π rad/sec
d) dφ=2π/dt = -8π/125
e) frequency = ω/2π = 8π/2π = 4Hz
f) deg = 180 φ/2π = 5.76 deg

y(t) = 6cos(8πt - 8π/125)


So i am not sure on my calculation for the phase shift.

Homework Statement





Homework Equations





The Attempt at a Solution


It is a typo in b) (period) but the result is correct. The "+" should be "-".

As for the phase constant: The signal has the form Acos(ωt+φ) It is maximum when ωt+φ=0, or integer times 2pi. Nearest to t=0, there is a maximum at t=-31.25 ms. Take ωt+φ=0, and substitute -31.25 for t.

ehild
 
Last edited:
  • #3
rude man
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Homework Statement


1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.

d) dφ=2π/dt = -8π/125 QUOTE]

What's this???
From the graph, we have 6cos(0.1ω0 + φ) = -6.
Solve for φ.
 

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