# Wave Problem - Phase Shift

## 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.

## 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.

## The Attempt at a Solution

#### Attachments

• Quest 1 Wave.png
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ehild
Homework Helper

## 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.

## 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.

## 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:
rude man
Homework Helper
Gold Member

## 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.