How Does Changing the Length of a Metal Strip Affect Its Resonance Frequency?

[dungarh]

Hey , I am not really the most brightest student when it comes to physics and i really don't understand it at all . but we are doing a prac in class and
here it is

Theory: A Clamped metal strip has a natural frequency of vibration which is related to its length. The shorter the leng, L the higher is its natural frequency.

Apparatus:
The metal strip you will use is part of an old ticker timer. This has an electromagnet in front of the clamp and a permanent magnet. When the electromegnet is connected to 4 Volt AC ( yellow terminals on power pack ) the metal strip is set vibrating at 50 Hz , Your task is to vary the length of the metal strip by shifting it in the clamp so that you acn adjust its natrual frequency to near 50 Hz. To make the results more clear you will take measurements of amplitude of vibration to near 50 Hz. To make the results more clear you will measurements of amplitude for different lengths. You will vary its length so that its natural freuqency varies either side of 50Hz .

thats what we're doing . can someone please help me with the results and what's going on in this prac ? so that i can understand what we're doing first then i can write up this prac.
thank you.

If anyone needs more info on the prac just ask and ill write up the procedure.

 

[tiny-tim]

Welcome to PF!

Hi dungarh! Welcome to PF!

The AC mains current goes on and off (in a sine wave) 50 times a second.

So the strip is being "hit" 50 times a second.

If you hit anything 50 times a second, it will go backwards and forwards 50 times a second … it has no choice …

but if you hit it just once, it will go backwards and forwards at its "natural" frequency.

The "natural" frequency depends on the length (and on density, thickness, etc), so you can change the "natural" frequency by changing the length.

So hit it once, giving it a bit of momentum, M, … then wait for it to complete a full cycle at its "natural" frequency … it will now have the same momentum, M, that you gave it … so now hit it with M again … that gives it double the momentum, 2M.

But, if you hit it with M the second time before (or after) a full cycle, its momentum will be less than M (it will even be negative, if you're more than a quarter of a cycle out), so the second M is added to less than M, making less than 2M.

The closer you are to the full cycle, the closer you get to 2M for the second time, 3M for the third time, and so on indefinitiely (obviously, there's energy loss eventually, so that's not entirely accurate, but you see the point ).

This is feedback.

The better you "tune" your strip, ie the closer its "natural" frequency is to 50 times a second, the bigger your feedback.