What affects the swing of a pendulum w/ and w/o air resistance

[The_Lobster]

Homework Statement

I'm having troubles figuring out what affects the swing of a pendulum.

Hypotheses:
1) The period is dependent on the amplitude
2) The period is dependent on the mass of the bob
3) Air resistance and friction will affect the period
4) The period is dependent on the length of the thread

Homework Equations

None...

The Attempt at a Solution

Well, as I've understood so far, hypothesis 1 is wrong, as a higher amplitude will give the bob greater kinetic energy, but the distance it has to travel is longer; hence they will cancel each other out and the period is the same?

Hypothesis 2: This one I'm having most trouble with. Without air resistance, any bob with any mass and density will travel with the same velocity. But with air resistance, is the period affected by the mass or by the density of the bob? Say the mass is constant but the density varies (big wood-bob 0.2 kg, small iron-bob 0.2 kg); will they both travel with the same velocity (w/ air resistance)? What about if the density is the same, but the mass varies (small iron bob 0.2 kg, large iron bob 1 kg)? What conclusions can be raised here? (some explanations as well would be great!)

Hypothesis 3: Well of course I guess? No need for further explanation?

Hypothesis 4: True. If we use the same amplitude on two bobs, one with a long thread the other with a short thread, the bob on the short thread will be in a higher position than the one with the long thread at the same amplitude, and therefore it will gain a higher kinetic energy than the other, though travel the same distance; hence quicker...

I guess it's hypothesis 2 I'm having most troubles with... It's probably very simple

Help please with confirming and correcting (especially hypothesis 2)? :)

Cheers,
Joachim

 

[Astronuc]

2. Homework Equations
None...

Hold on there - a swinging pendulum is an example of simple harmonic motion, and there is a basic equation with and without damping (air resistance is a damping mechanism). Understanding this equation will give insight into the answers to the questions posed.

http://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permot

http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

for a spring - http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html

 

[m2003]

It appears that you have some good hypotheses and are on the right track in understanding the factors that affect the swing of a pendulum. Here are some points to consider:

1. The period of a pendulum is indeed dependent on the amplitude. As you mentioned, a higher amplitude will result in a longer distance for the bob to travel, but it will also result in a larger angle of displacement, which affects the restoring force and therefore the period.

2. The mass of the bob does not affect the period of a pendulum in the absence of air resistance. This is because, as you correctly stated, all objects will fall with the same acceleration due to gravity regardless of their mass. However, when air resistance is present, the mass and density of the bob can affect the period. This is because the air resistance will create a drag force that is proportional to the surface area and velocity of the bob. A denser bob with a larger surface area will experience more drag and therefore have a longer period compared to a less dense bob with a smaller surface area.

3. As you mentioned, air resistance and friction will definitely affect the period of a pendulum. In the presence of air resistance, the amplitude will gradually decrease due to the loss of energy to air resistance and friction, resulting in a shorter period.

4. The length of the thread or string does affect the period of a pendulum. A longer thread will result in a longer period, as the bob has to travel a greater distance to complete a swing.

Overall, it is important to consider all the factors that can affect the period of a pendulum, including air resistance, friction, amplitude, mass, and length of the string. It is also important to note that these factors can interact with each other and may not always have a straightforward relationship. Keep exploring and experimenting to deepen your understanding of pendulum motion.