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Squenay mathematics
Just take some points and follow the definition. There is no good way. Mainly when w= 1 infinity, it should be divided into two parts;

General shape analysis:

When w=0, no integral starts from the positive real axis 1; The second-order undamped phase angle changes at the frequency 1, so w

When w= 1+, the amplitude is infinite and the phase angle is-180-45=-225 degrees; When w is not too large, the amplitude is very small, and the final phase angle is-270.

Summary: The curve starts from 1, decreases slightly, and then turns to -45, tending to infinity. When w= 1+, -225 degrees tends to infinity, and when w is infinite, it tends to the origin and the direction is -270 degrees. This section should be close to a straight line, and the angle near the origin will change.

When w= 1, the phase angle suddenly changes-180 degrees. This kind of question has no practical significance, just playing with high school mathematics.