A particle of mass $m$ is located in a field such that its potential energy is given by $U\left(x\right)=U_0\left(1-\text{cos}ax\right)$ where $U_0$ and $a$ are positive constants. The period of small oscillations is

• A

  $2\pi \sqrt{\frac{U_0}{m{a}^2}}$
• B

  $2\pi \sqrt{\frac{m{U}_0}{a^2}}$
• C

  $2\pi \sqrt{\frac{a_0}{m{U}_0}}$
• Correct answer
  D

  $2\pi \sqrt{\frac{m}{U_0{a}^2}}$

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