$$\begin{align*} m \ddot{x} &= \ddot{x} = -\frac{d}{dx} \left(V_{\text{MT}}(x) + V_{\text{sech}}(x-\xi) \right) \\ V_{\text{MT}}(x) &= \frac{1}{2} \Omega^2 x^2 = \frac{1}{2} x^2\\ V_{\text{sech}}(x-\xi) &= A^{2} \operatorname{sech}^{2}\left(A \left(x - {\xi}\right)\right) = \operatorname{sech}^{2}\left(\left(x - {\xi}\right)\right)\\ \end{align*}$$

$$\begin{align*} A &= 1 \\ m &= 1 \\ \Omega &= 1 \\ x(0) &= x_0 \\ \xi(0) &= 0 \\ \dot{x}(0) &= 0 \\ x(t = T_{\text{th}}) &= x^* = 0.5 \\ \xi(t = T_{\text{th}}) &= x^* = 0.5 \\ |\dot{x}(t = T_{\text{th}})| &\leq 0.01\\ T_{\text{th}} &= 10\text{ seconds} \\ \end{align*}$$