The equation of the displacement of two particles making SHM are represented by y1=a sin(ω t+φ)y2=a cos(ω t) The phase difference of the velocities of the two particles is

Question

The equation of the displacement of two particles making SHM are represented by y1=a sin(ω t+φ)y2=a cos(ω t) The phase difference of the velocities of the two particles is (A) (π/2)+φ (B) -φ (C) φ (D) φ-(π/2)

Tardigrade Admin · Accepted Answer

y 1=a sin(ω t +φ) y 2=a cos(ω t ) y 1=a ω cos (ω t +φ) =a ω sin (ω t +φ+π / 2) y 2=- a ω sin (ω t )= a ω sin (π+ω t ) therefore phase difference =ω t +φ+π / 2-(π+ω t ) =φ-π / 2

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

$\frac{π}{2} + ϕ$

$- ϕ$

$ϕ$

$ϕ - \frac{π}{2}$

$y_{1} = a sin (ω t + ϕ)$
$y_{2} = a cos (ω t)$
$y_{1} = aω cos (ω t + ϕ)$
$= aω sin (ω t + ϕ + π /2)$
$y_{2} = - aω sin (ω t) = aω sin (π + ω t)$
therefore phase difference $= ω t + ϕ + π /2 - (π + ω t)$
$= ϕ - π /2$

Q. The equation of the displacement of two particles making SHM are represented by y1​=asin(ωt+ϕ)y2​=acos(ωt) The phase difference of the velocities of the two particles is

2π​+ϕ

−ϕ

ϕ

ϕ−2π​

y1​=asin(ωt+ϕ) y2​=acos(ωt) y1​=aωcos(ωt+ϕ) =aωsin(ωt+ϕ+π/2) y2​=−aωsin(ωt)=aωsin(π+ωt) therefore phase difference =ωt+ϕ+π/2−(π+ωt) =ϕ−π/2

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

$\frac{π}{2} + ϕ$

$- ϕ$

$ϕ$

$ϕ - \frac{π}{2}$

$y_{1} = a sin (ω t + ϕ)$
$y_{2} = a cos (ω t)$
$y_{1} = aω cos (ω t + ϕ)$
$= aω sin (ω t + ϕ + π /2)$
$y_{2} = - aω sin (ω t) = aω sin (π + ω t)$
therefore phase difference $= ω t + ϕ + π /2 - (π + ω t)$
$= ϕ - π /2$