Simple Harmonic Motion experiment help

[incalculable]

I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link.

http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc.

I have two questions!

Question 1:when i did the experiment, I found that with a greater length (L), the depression (y) was also greater (the weight was constant).

So the question is,WHY would the depression would increase as the length increases.

Question 2:We were also told to pull the mass down, and then release it. This resulted in the ruler oscillating up and down - exhibiting simple harmonic motion.
I found that (when the weight is constant) when you decrease the length (L), the time period of oscillations decreased, and so the frequency increased.

I again want to know WHY the frequency increased as length decreases.

NOTE:The attachment was just there to clarify what the experiment setup was like, as i felt i wouldn't be able to explain it well. In reality we only measured the change in depression (y) as the length (L) increased and how the frequency changed with increasing length (L) (when we displaced the masses). We always used a constant mass of 1kg.
The questions 1 and 2 that i have asked are things I don't understand myself.If someone could also provide equations to help explain the results i would be extreeeeemely grateful!

 

[CWatters]

Hint: Levers.

 

[incalculable]

so, are you implying its to do with moments?

 

[haruspex]

so, are you implying its to do with moments?

Yes.

 

[HalfLostAndSearching]

I am happy to help you understand the results of your experiment. Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. In your experiment, the ruler acts as a simple harmonic oscillator.

To answer your first question, the depression (y) increases as the length (L) increases because of the relationship between the length and the period of oscillation. The period of oscillation (T) is the time it takes for the ruler to complete one full cycle of oscillation. It is given by the equation T = 2π√(L/g), where g is the acceleration due to gravity. As you can see, the period is directly proportional to the square root of the length. This means that as the length increases, the period also increases, resulting in a greater depression (y) before the mass comes to rest.

Now, for your second question, the frequency of oscillation (f) is the number of cycles per unit time and is given by the equation f = 1/T. As we saw earlier, the period is directly proportional to the square root of the length. This means that as the length decreases, the period also decreases, resulting in an increase in frequency. This is because the time it takes for one cycle to complete is shorter for a shorter length, so there are more cycles per unit time.

In summary, the increase in depression (y) with increasing length (L) is due to the relationship between length and period, while the increase in frequency with decreasing length is due to the relationship between length and period.

I hope this explanation helps you understand the results of your experiment. As for the equations, I have provided them above. You can also do some further research on simple harmonic motion to gain a deeper understanding of the concepts involved. Keep up the good work in your scientific endeavors!