what the relation between the amplitude magnitude and mass at resonance?

[kirito]

should I be expecting a higher amplitude at resonance for a mass that's heavier to an extent form another where each is attached to a spring vertically , I assumed that's true since the heavier mass will stretch the spring more meaning when moving like a sin or cos wave the amplitude magnitude will be higher and indeed that was the result I got for 2 different masses, is there any other interpretations , and is this reason unreasonable for predicting the result ? what I am curious about is according to how the amplitude solution that I got seemed to indicate as mass increase but the amplitude in the the equation for ( simple harmonic motion under a force seems to imply the the amplitude gets lower with higher masses

 

[berkeman]

Please describe the complete experiment, including how the mass is driven in the oscillation. Please provide much more information so we can try to interpret your results.

What equations are you using to try to predict your results?

Also, is this for schoolwork? If so, I can move this thread to the schoolwork forums.

 

[kirito]

Please describe the complete experiment, including how the mass is driven in the oscillation. Please provide much more information so we can try to interpret your results.

What equations are you using to try to predict your results?

Also, is this for schoolwork? If so, I can move this thread to the schoolwork forums.

hi I actually also wondered where is this more appropriately placed , we had to do an experiment regarding simple harmonic motion and write a report about it but this part was extra I just added it from my own violation since I was interested in checking if the results, I will get align with what I expect and if they do would this align but for the wrong reasons

 

[kirito]

as for the whole experiment ,we were studying the behaviour of oscillatory systems subjected to an external force and observing the link between the frequency of the applied force and the amplitude of the system, as well as what maximizes it.

We start out our experiment by selecting two distinct masses: one weighing 77.95 grams and the other 37.72 grams. In each graph we made multiple measurements
-18,13 respectively- of the amplitude (on the y axis ) as a function of frequency ( on the x axis) with an error on the vertical axis of 0.03mm

to find the frequency of resonance I started by making a guess of f= natural frequency of the system /2pi

from there checking near the area if I got the maximum amplitude to make sure there won't be another maximum near the area I also check some farther region , the reason I made this guess is assuming the push by the force given would be given when the maximum amplitude of the system was reached so it will farther amplify it ,where as a push before or after is supposed to interfere with the original cycle of the wave pushing it back at some parts causing a lower amplitude,

I wanted to farther research this matter by checking if after enough time the initial condition of the system won't or will effect the amplitude (like is we start applying a force on it from rest or we pull it down (the mass)then apply the force , and reached results showing that they won't , which I expected to an extent from the equations , I also tried to check the relation between the results of the two masses why the larger mass resulted in a higher amplitude , and what causes the symmetry around the maximum , to explain this I just went on to explain how our function is even yet the definition of even is around the origin this is not about the origin so I noted it should be farther investigated




to clear the experiment a bit the masses were attached to a spring vertically and there is a device the apples a force with the frequency of our choice we set the device to 1 volt and the result are as provided in the graph

 

[kirito]

the equations I used $$x=a*sin(\omega *t +\phi)+c$$ after enough time for getting the movement of every wave , the amplitude was gotten through the graphs by checking the peaks average in the stable condition

 

[kirito]

second equation
$$amplitude(\omega_{drive})=\frac{\frac{force _{drive}}{m}}{4*\pi^2*\sqrt{\frac{tao*\omega_{drive}}{2}^2+\omega_{natural}^2 +\omega_{drive}^2}$$
this for getting the amplitude as a function of frequency we actually used it to find the value of the force on each mass