AP EAPCET 24-Aug-2021 Shift 1 Paper

Given that, two particles P and Q describes
SHM of same amplitude a and frequency f.
Let equation of motion of two particles are
x1=a‌sin‌ω‌t and x2=a‌sin(ωt+ϕ)
where, ϕ be the phase difference.
∴ Path difference,
x2−x1=a‌sin(ωt+ϕ)−a‌sin‌ω‌t [Using identity sin‌A−sin‌B=2‌sin(

A−B

2

).cos(

A+B

2

)]
∴ x2−x1=2a‌sin(

ϕ

2

)‌cos(ω+

ϕ

2

)
The distance x2−x1 will be maximum when cos(ωt+

ϕ

2

)=1
∴ Maximum distance
x2−x1=√2a
=2a‌sin‌

ϕ

2

⇒sin‌

ϕ

2

=

1

√2

⇒sin‌

ϕ

2

=sin‌45°
⇒

ϕ

2

=45°
Phase difference, ϕ=90°=

π

2