How do I deal with square, cubic, etc. zeros and poles when manually drawing a Bode Plot?
The slope change is 20dB/decade multiplied by the order (squared, cubed, etc.) of the pole or zero. The pole at \$\omega_C = 50 rad/s\$ would change the slope by -40dB/decade. The same applies for the phase: the mentioned pole would shift it by -90deg/decade (\$2\times-45deg/dec\$), starting one decade earlier.