AP EAMCET Engineering 23 Sep 2020 Shift 1 Paper

Let say displacement-time equation of a particle executing SHM starting from mean position is as follow
x=A‌sin‌ω‌t....(i)
The time taken by it to go from x=0 to x=‌

A

2

is T1, then
‌

A

2

=A‌sin‌ω‌T1
‌

1

2

=sin‌ω‌T1
or sin‌

π

6

=sin‌ω‌T1
or ωT1=‌

π

6

...(ii)
Now, the time taken by the particle to go from x=‌

A

2

to x=A is T2, then time taken from x=0 to x=A is (T1+T2). So, we may write using Eq. (i)
A=A‌sin{ω(T1+T2)}
or 1=sin{ω(T1+T2)}
or sin‌

π

2

=sin{ωT1+ωT2}
Or ωT1+ωT2=‌

π

2

or ωT2+‌

π

6

=‌

π

2

[from Eq. (ii)]
or ωT2=‌

π

3

....(iii)
From Eqs. (ii) and (iii), we get
‌

ωT1

ωT2

=‌

π∕6

π∕3

=‌

1

2

⇒‌‌‌

T1

T2

=‌

1

2

⇒T1<T2