Harmonic Motion in Earth and Moon: A Comparative Study

In summary, a mass suspended on a vertical string executes an harmonic motion with a period that is longer on the moon due to the smaller gravitational force. The amplitude of the motion is also the same.
  • #1
SciencePF
56
0
Suppose that, on Earth, a mass is suspended on a vertical string and is executing an harmonic motion with
Period: T
Amplitude: A
Angular frequency: [tex]\omega[/tex]

Now all the system is put in the Moon. What changes that system will have?

Thanks for you help
 
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  • #2
Recall that the period of simple harmonic motion is
c64bc6d20c9b05eb08dddb30f639d70a.png
, and so depends on gravity (g). Since gmoon is smaller than gearth, the period will be greater.
 
  • #3
And what goes to happen with the amplitude of motion? Equal on Earth and Moon?
 
  • #4
Yes, the amplitude in this case is arbitrary, it just equals A. In other words if you start a pendulum swinging on Earth by pulling it to A, then go to the moon and start it again by pulling it to A, the difference is in the period (which gets longer by the relationship above).

If you do the same experiment but want to keep the period constant, then you'll need to swing a shorter amplitude on the moon.
 
  • #5
But, in this site, has a simulation, and things don't work as you said!
http://www.walter-fendt.de/ph14e/springpendulum.htm"
 
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  • #6
SciencePF said:
But, in this site, has a simulation, and things don't work as you said!
http://www.walter-fendt.de/ph14e/springpendulum.htm"

I think that you mean this simulation:
http://www.walter-fendt.de/ph14e/pendulum.htm

The spring pendulum carries the spring constant wherever it goes.
 
Last edited by a moderator:
  • #7
My initial question,
-----------------------------------
Suppose that, on Earth, a mass is suspended on a vertical string and is executing an harmonic motion with
Period: T
Amplitude: A
Angular frequency: [tex]\omega[/tex]
Now all the system is put in the Moon. What changes that system will have?
--------------------------------------
are about this simulation:
http://www.walter-fendt.de/ph14e/springpendulum.htm"

It seems no change will occur.

Sorry, for this post and thanks for your collaboration.
 
Last edited by a moderator:

1. What is SHM (Simple Harmonic Motion) in Earth and Moon?

Simple Harmonic Motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and frequency. In the context of Earth and the Moon, this motion is seen in the movement of tides, which are caused by the gravitational pull of the Moon and the Sun on the Earth's oceans.

2. How does the SHM in the Earth differ from that in the Moon?

The main difference between SHM in the Earth and the Moon is the size of the oscillation. Due to its larger mass and gravitational pull, the Earth experiences larger tides compared to the Moon. Additionally, the Earth's rotation also affects the tides, causing them to occur twice a day, while the Moon's rotation causes tides to occur once a day.

3. What are the factors that affect SHM in Earth and Moon?

The main factors that affect SHM in Earth and Moon are the mass, distance, and rotational speed of the objects. The larger the mass and closer the distance between the objects, the stronger the gravitational pull and the larger the oscillation. The rotational speed also plays a role in the frequency of the oscillation.

4. How does the SHM in Earth and Moon impact life on Earth?

The SHM in Earth and Moon, specifically the tides, play a crucial role in the ecosystem and life on Earth. Tides help to mix and distribute nutrients in the ocean, which is essential for marine life. They also affect coastal ecosystems and provide a source of energy for activities like tidal power generation.

5. Can SHM in Earth and Moon be predicted?

Yes, SHM in Earth and Moon can be predicted using mathematical models and equations based on the factors mentioned earlier. Scientists can accurately predict the timing and height of tides, which is important for industries such as fishing and shipping. However, factors such as weather and changes in the Earth's rotation can affect the accuracy of these predictions.

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