AP EAPCET 04-Jul-2022 Shift 2 Paper

(c) According to first condition, In S. H. M, at displacement x
Potential energy =9J
i.e, ‌‌‌

1

2

kx2=9.......(i)
Again, at displacement y,
Potential energy
‌

1

2

ky2=16.......(ii)
Dividing Eq. (ii) by Eq. (i), we get
‌

‌ 1 2 ky2

1 2 kx2

‌=‌

16

9

⇒‌‌(‌

y

x

)2‌=(‌

4

3

)2
‌

y

x

‌=‌

4

3

.......(iii)
∵ Potential energy of body at displacement (x+y)
‌ PE ‌‌=‌

1

2

k(x+y)2
‌=‌

9

x2

(x+y)2‌‌‌ [From Eq. (i) ] ‌
‌=9‌

(x+y)2

x2

=9(1+‌

y

x

)2
‌=9(1+‌

4

3

)2‌‌‌ [From Eq. (iii)] ‌
‌=49J