A string of mass per unit length $\mathrm{\mu }$ is clamped at both ends such that one end of the string is at $\mathrm{x} = 0$ and the other is at $\mathrm{x} = \mathrm{L}$. When the string vibrates in fundamental mode, the amplitude of the mid-point $\mathrm{O}$ of the string is $\mathrm{a}$, and tension in the string is $\mathrm{T}$, Find the total oscillation energy stored in the string.

• Correct answer
  A

  $\frac{{\pi }^2{a}^2\text{T}}{4\text{L}}$
• B

  $\frac{{\pi }^{\mathrm{}}{a}^{\mathrm{}}\text{T}}{2\text{L}}$
• C

  $-\frac{{\pi }_2{a}_2\text{T}}{3\text{L}}$
• D

  $\frac{{\pi }^2{a}^{\mathrm{}}\text{T}}{6\text{L}}$

Hence, the correct answer is option: 'A'.