TG EAMCET 2 May 2025 Shift 1 Paper

Given:
‌

U

K

=‌

4

5

The amplitude A=6cm
Step 1: Write the energy formulas
The total energy is E=‌

1

2

kA2
The potential energy is U=‌

1

2

kx2
The kinetic energy is K=‌

1

2

k(A2−x2)
Step 2: Set up the given ratio
We want the distance x from the mean position so that ‌

U

K

=‌

4

5

:
‌

‌ 1 2 kx2

1 2 k(A2−x2)

=‌

4

5

Step 3: Simplify the equation
The ‌

1

2

k cancels out: ‌

x2

A2−x2

=‌

4

5

Step 4: Solve for x2
Multiply both sides by (A2−x2):5x2=4(A2−x2)
Expand: 5x2=4A2−4x2
Bring 4x2 to the left: 5x2+4x2=4A2
Combine like terms: 9x2=4A2
Step 5: Find x
Divide both sides by 9: x2=‌

4

9

A2
Take the square root: x=‌

2

3

A
Since A=6cm :
x=‌

2

3

×6=4cm
The distance from the mean position is 4 cm .