\omega^{(n)}_{L,R} = e^{\frac{5}{2}A(y)} e^{\frac{5\kappa}{4\sqrt{3}}\big(<\Phi>+\xi(y)\big)}\zeta^{(n)}_{L,R}
   \label{rescale}
  \end{aligned}$$

we find that the two helicity states, $\zeta_L$ and $\zeta_R$ satisfy the same equation of motion and is given by, $$\begin{aligned}
   &\frac{\partial^2\omega^{(n)}}{\partial y^2}& + e^{-\frac{\kappa}{\sqrt{3}}\big(<\Phi>+\xi(y)\big)}\bigg[e^{\frac{\kappa}
   {\sqrt{3}}\big(<\Phi>+\xi(y)\big)} \bigg(-\frac{1}{4}A'^2 - \frac{\kappa^2}{48}\xi'^2\nonumber\\ 
   &-&\frac{\kappa}{4\sqrt{3}}A'\xi' + m_{n}^2e^{2A(y)}\bigg) + m_5^2\bigg] \omega_{L,R} = 0
   \label{reduced eom}
  \end{aligned}$$

Using the forms of $A(y)$ and $\xi(y)$, we obtain the solution of eqn.(\[reduced eom\]) and is given by Hypergeometric function as follows : $$\begin{aligned}
   &\zeta&^{(n)}_{L,R}(y) = \sqrt{k} \exp{\bigg[-\frac{p}{8k}e^{(2+\nu)ky}\bigg]}*\nonumber\\
   &\exp&{\bigg[-\frac{1}{8k}\sqrt{q^2e^{4(2+\nu)ky}+k^2+4m_{n}^2e^{2ky}+4m_5^2}\bigg]}*
   HypergeometricU\bigg[\frac{5}{8}\nonumber\\
   &+&\frac{qe^{2(2+\nu)ky}}{8k} + \frac{\sqrt{q^2e^{4(2+\nu)ky}+k^2+4m_{n}^2e^{2ky}+4m_5^2}}{8k},\nonumber\\
   &1&+ \frac{\sqrt{q^2e^{4(2+\nu)ky}+k^2+4m_{n}^2e^{2ky}+4m_5^2}}{4k},\frac{p}{4k}e^{(2+\nu)ky}\bigg]
   \label{solution3}
  \end{aligned}$$

The mass spectrum can be obtained from the requirement that the wave function is well behaved on the brane. Demanding the continuity of $\xi_{L,R}$ at $y=0$ and at $y=\pi r_c$, the KK mass term can be obtained as follows : $$\begin{aligned}
    m_n^2&=&e^{-2A(\pi r_c)} e^{-\frac{\kappa}{\sqrt{3}}\big(<\Phi>+\xi(\pi r_c)\big)} \bigg[k^2(n^2 + 2n + 1) + m_5^2\bigg]
    \label{mass spectrum}
   \end{aligned}$$ where $n=1,2,3....$. The above expression of mass spectrum is in agreement with [@jm].\
Now from the requirement of resolving the gauge hierarchy problem, the warp factor at TeV brane acquires the value $= 36$ which produces a large suppression in the right hand side of eqn. (\[mass spectrum\]) through the exponential factor. Since $k, m_5\sim M$, the mass of KK modes ($n=1,2,3..$) 