KCET 2025 Physics Paper

To understand the displacement x0 where kinetic energy (KE) equals potential energy (PE) in simple harmonic motion (SHM), consider the following explanation:
At the position x0, the kinetic energy is equal to the potential energy. Mathematically, this is represented by:
‌

1

2

mω2(A2−x2)=‌

1

2

mω2x2
Here, the left side of the equation represents the kinetic energy, and the right side represents the potential energy. Simplifying the equation:
A2−x2=x2
Rearranging terms, we get:
A2=2x2
Solving for x :
‌x2=‌

A2

2

‌x=‌

A

√2

Thus, the value of |x0| is ‌

A

√2

.