What is the phase difference between two simple harmonic motions represented by $x_{1} = A sin (ω t + \frac{π}{6})$ and $x_{2} = A cos (ω t)$ ?

Name: What is the phase difference between two simple harmonic motions represented by x1 = Asin (ω t + pi6 ) and x2 = A cos (ω t) ?
Uploaded: 2020-01-06
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Question

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Answer 1

Given,
$x_{1} = A sin (ω t + \frac{π}{6})$
$x_{2} = A cos (ω t)$
$x_{2} = A sin (ω t + \frac{π}{2})$

Phase difference:
$△ ϕ = ϕ_{2} - ϕ_{1}$

$△ ϕ = \frac{π}{2} - \frac{π}{6}$

$△ ϕ = \frac{3 π - π}{6} = \frac{π}{3}$

Answer 2

Given,

x_{1} = A sin (ω t + \frac{π}{6})

x_{2} = A cos (ω t)

x_{2} = A sin (ω t + \frac{π}{2})

Phase difference:

△ ϕ = ϕ_{2} - ϕ_{1}

△ ϕ = \frac{π}{2} - \frac{π}{6}

△ ϕ = \frac{3 π - π}{6} = \frac{π}{3}

What is the phase difference between two simple harmonic motions represented by $x_{1} = A sin (ω t + \frac{π}{6})$ and $x_{2} = A cos (ω t)$ ?

$\frac{π}{6}$

$\frac{π}{3}$

$\frac{π}{2}$

$\frac{2 π}{3}$

Given,
$x_{1} = A sin (ω t + \frac{π}{6})$
$x_{2} = A cos (ω t)$
$x_{2} = A sin (ω t + \frac{π}{2})$

Phase difference:
$△ ϕ = ϕ_{2} - ϕ_{1}$

$△ ϕ = \frac{π}{2} - \frac{π}{6}$

$△ ϕ = \frac{3 π - π}{6} = \frac{π}{3}$

The displacement equations of two simple harmonic oscillators are given by $x_{1} = A_{1} cos ω t$ ; $x_{2} = A_{2} sin (ω t + \frac{π}{6})$ . The phase difference between them is:

Two simple harmonic motions are given by $y_{1} = a sin [(\frac{π}{2}) t + ϕ]$ and $y_{2} = b sin [(\frac{2 π}{3}) t + ϕ]$ . The phase difference between these after 1 s is:

A point mass oscillates along the x-axis according to the law $x = x_{0} c o s (ω t - \frac{π}{4})$ . If the acceleration of the particle is written as $a = A c o s (ω t + δ)$ , then

The equation of the displacement of two particles making SHM are represented by
$y_{1}$ = a sin $(ω t + ϕ)$ & $y_{2}$ = a cos $(ω t)$ .
The phase difference of the velocities of the two particles is :

The minimum phase difference between two SHM's is:
$y_{1} = sin (\frac{π}{6}) sin (ω t) + sin (\frac{π}{3}) cos (ω t)$

$y_{2} = cos (\frac{π}{6}) sin (ω t) + sin (\frac{π}{3}) cos (ω t)$ is:

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What is the phase difference between two simple harmonic motions represented by x1​=Asin(ωt+6π​) and x2​=Acos(ωt)?

6π​

3π​

2π​

32π​

Given, x1​=Asin(ωt+6π​) x2​=Acos(ωt) x2​=Asin(ωt+2π​) Phase difference: △ϕ=ϕ2​−ϕ1​ △ϕ=2π​−6π​ △ϕ=63π−π​=3π​

The displacement equations of two simple harmonic oscillators are given by x1​=A1​cosωt; x2​=A2​sin(ωt+6π​). The phase difference between them is:

Two simple harmonic motions are given by y1​=asin[(2π​)t+ϕ] and y2​=bsin[(32π​)t+ϕ]. The phase difference between these after 1 s is:

A point mass oscillates along the x-axis according to the law x=x0​cos(ωt−4π​). If the acceleration of the particle is written as a=Acos(ωt+δ), then

The equation of the displacement of two particles making SHM are represented by y1​ = a sin (ωt+ϕ) & y2​ = a cos (ωt). The phase difference of the velocities of the two particles is :

The minimum phase difference between two SHM's is: y1​=sin(6π​)sin(ωt)+sin(3π​)cos(ωt) y2​=cos(6π​)sin(ωt)+sin(3π​)cos(ωt) is:

Revise with Concepts

Displacement Relation in a Progressive Wave

Amplitude and Phase of a Progressive Wave

Wavelength and Angular Wave Number of a Progressive Wave

Period, Angular Frequency and Frequency of a Progressive Wave

What is the phase difference between two simple harmonic motions represented by $x_{1} = A sin (ω t + \frac{π}{6})$ and $x_{2} = A cos (ω t)$ ?

$\frac{π}{6}$

$\frac{π}{3}$

$\frac{π}{2}$

$\frac{2 π}{3}$

Given,
$x_{1} = A sin (ω t + \frac{π}{6})$
$x_{2} = A cos (ω t)$
$x_{2} = A sin (ω t + \frac{π}{2})$

Phase difference:
$△ ϕ = ϕ_{2} - ϕ_{1}$

$△ ϕ = \frac{π}{2} - \frac{π}{6}$

$△ ϕ = \frac{3 π - π}{6} = \frac{π}{3}$

The displacement equations of two simple harmonic oscillators are given by $x_{1} = A_{1} cos ω t$ ; $x_{2} = A_{2} sin (ω t + \frac{π}{6})$ . The phase difference between them is:

Two simple harmonic motions are given by $y_{1} = a sin [(\frac{π}{2}) t + ϕ]$ and $y_{2} = b sin [(\frac{2 π}{3}) t + ϕ]$ . The phase difference between these after 1 s is:

A point mass oscillates along the x-axis according to the law $x = x_{0} c o s (ω t - \frac{π}{4})$ . If the acceleration of the particle is written as $a = A c o s (ω t + δ)$ , then

The equation of the displacement of two particles making SHM are represented by
$y_{1}$ = a sin $(ω t + ϕ)$ & $y_{2}$ = a cos $(ω t)$ .
The phase difference of the velocities of the two particles is :

The minimum phase difference between two SHM's is:
$y_{1} = sin (\frac{π}{6}) sin (ω t) + sin (\frac{π}{3}) cos (ω t)$

$y_{2} = cos (\frac{π}{6}) sin (ω t) + sin (\frac{π}{3}) cos (ω t)$ is: