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

Question

What is the phase difference between two simple harmonic motions represented by x1-Asin-t-6- and x2-Acos-t-

Toppr Admin · Accepted Answer

Given-x1-Asin-x3C9-t-x3C0-6-x2-Acos-x3C9-t-x2-Asin-x3C9-t-x3C0-2-Phase difference-x25B3-x3D5-x3D5-2-x2212-x3D5-1-x25B3-x3D5-x3C0-2-x2212-x3C0-6-x25B3-x3D5-3-x3C0-x2212-x3C0-6-x3C0-3

What is the phase difference between two simple harmonic motions represented by x1=Asin(ωt+π6) and x2=Acos(ωt)?

Given,x1=Asin(ωt+π6)x2=Acos(ωt)x2=Asin(ωt+π2)Phase difference:△ϕ=ϕ2−ϕ1△ϕ=π2−π6△ϕ=3π−π6=π3

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

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:
$△ ϕ = ϕ_{2} - ϕ_{1}$

$△ ϕ = \frac{π}{2} - \frac{π}{6}$

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