TS EAMCET 6-Aug-2021 Shift 2 Question Paper

The two SHM have same amplitude and same frequency.
∴ Let x1=a‌sin‌ω‌t
and x2=a‌sin(ωt+θ)
(where, φ is the phase difference.)
When they cross each other, x1=x2=‌

a

2

At x1=‌

a

2

, we get, ‌

a

2

=a‌sin‌ω‌t
⇒sin‌ω‌t=‌

1

2

=sin‌

π

6

⇒ωt=‌

π

6

At x2=‌

a

2

, we get, ‌

a

2

=a‌sin(ωt+φ)
⇒‌‌sin(ωt+φ)=‌

1

2

=sin‌

π

6

or sin‌

5π

6

∴‌‌ωt+φ=‌

π

6

or ‌

5π

6

(i) When ωt+φ=‌

π

6

,
then, ‌‌φ=‌

π

6

−ωt=‌

π

6

−‌

π

6

=0
which is not possible.
(ii) When ωt+φ=‌

5π

6

,
then φ=‌

5π

6

−‌

π

6

=‌

4π

6

=‌

2π

3

∴‌‌φ=‌

2π

3