The paper investigates the excitation of quadratic quasinormal modes (QNMs) for Kerr black holes, focusing on the linear mode $(l = m = 2, n = 0)$. The authors compute the ratio of the amplitude of the second-order effect to the linear mode amplitude, which is proportional to the square of the linear mode amplitude. This ratio is found to depend on the dimensionless spin of the black hole, ranging up to 0.99. The study employs the frequency-domain second-order Teukolsky equation, involving two key steps: analytically reconstructing the metric using the Chrzanowski-Cohen-Kegeles (CCK) approach and numerically solving the equation using the shooting method along a complex contour. The results show that the spin dependence of the ratio is strongly correlated with the angular overlap between the parent and child modes, providing insights into the nature of Kerr black holes. The findings have implications for the search for quadratic QNMs from numerical relativity and gravitational wave detections. Additionally, the paper demonstrates that the Weyl scalars can be expressed concisely in terms of the Hertz potential.The paper investigates the excitation of quadratic quasinormal modes (QNMs) for Kerr black holes, focusing on the linear mode $(l = m = 2, n = 0)$. The authors compute the ratio of the amplitude of the second-order effect to the linear mode amplitude, which is proportional to the square of the linear mode amplitude. This ratio is found to depend on the dimensionless spin of the black hole, ranging up to 0.99. The study employs the frequency-domain second-order Teukolsky equation, involving two key steps: analytically reconstructing the metric using the Chrzanowski-Cohen-Kegeles (CCK) approach and numerically solving the equation using the shooting method along a complex contour. The results show that the spin dependence of the ratio is strongly correlated with the angular overlap between the parent and child modes, providing insights into the nature of Kerr black holes. The findings have implications for the search for quadratic QNMs from numerical relativity and gravitational wave detections. Additionally, the paper demonstrates that the Weyl scalars can be expressed concisely in terms of the Hertz potential.