Can someone explain General Forced Response from Mechanical Vibrations!

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Ive been going through my textbook but I cant understand a bit of what they’re saying.

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Okay, so if you shake something, it’s going to move. But how much it moves depends on some stuff. So suppose you take a long thin pole and grab it by the middle and shake it. The ends will move a lot. If you try various speeds that you shake it at, you’ll find that some speeds it moves more and some speeds it moves less. What is happening is that the pole has some natural frequencies that it wants to vibrate at due to length and stiffness.

So general forced response is taking the natural vibration modes of the object and figuring out that some vibrations will match well with the natural modes and the movement will get more and that some will not match and movement will be less and that some will cancel out and not much movement will happen at all.

So the math is to take the expression for the natural vibration and grinding it against the excitation to see how much things move.