What is the connection between simple harmonic motion and pendulum motion?

In summary, simple harmonic motion and pendulum motion are connected by the fact that they both have a restoring force that is proportional to the displacement from equilibrium. However, in the case of a pendulum, this force is not directly in the opposite direction of the displacement and the motion is only approximately simple harmonic when a specific condition is met.
  • #1
AnthroMecha
26
0

Homework Statement



What is the connection between simple harmonic motion and pendulum motion?


Homework Equations



Harmonic motion period=T=2piroot(m/k)
Pendulum motion period=T=2piroot(L/g)

The Attempt at a Solution



Conservation of momentum??

Thanks for any help!
 
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  • #2
I strongly suggest reading the Wikipedia article on simple harmonic motion.
Consider comparing the equation of motion for the general SHM and the pendulum, that is the formula relating angle or displacement to time.
 
  • #3
Delphi51 said:
I strongly suggest reading the Wikipedia article on simple harmonic motion.
Consider comparing the equation of motion for the general SHM and the pendulum, that is the formula relating angle or displacement to time.

Thanks for pointing me in the right direction. This is what I came up with:

A pendulum oscillates in a simple harmonic motion like that of an oscillating spring. The angle θ in pendulum motion is relative to the distance x that a spring is stretched by a mass (m) and a gravity (g).
 
  • #4
Pretty good. But isn't SHM a general concept of which the pendulum, spring, water waves, radio waves, etc. are all specific examples? For the word "connection" in the question, I would look for what makes the pendulum simple harmonic, both from the motion characteristics and the nature of the force that causes the motion.
 
  • #5
Delphi51 said:
Pretty good. But isn't SHM a general concept of which the pendulum, spring, water waves, radio waves, etc. are all specific examples? For the word "connection" in the question, I would look for what makes the pendulum simple harmonic, both from the motion characteristics and the nature of the force that causes the motion.

Hmmm...a restoring force in the opposite direction of displacement is what makes it a SHM, right? and in the case of the pendulum mg is the restoring force?
 
  • #6
The restoring force has to have a specific formula. . .
Yes, mg is the driving force, but it isn't in the right direction, is it? The pendulum restoring force is a little bit complex, and when you get into the details it is only approximately the right formula, so the pendulum only has nearly SHM when a particular condition is met. No doubt you can look up all that if you want to give a great answer.
 
  • #7
Thanks for the help Delphi!
 
  • #8
Most welcome!
 

1. What is simple harmonic motion?

Simple harmonic motion is the repetitive back and forth motion of an object around its equilibrium position, caused by a restoring force that is proportional to the displacement from equilibrium. It is a type of periodic motion that can be described using a sinusoidal function.

2. How does a pendulum exhibit simple harmonic motion?

A pendulum exhibits simple harmonic motion because it experiences a restoring force (gravity) that is proportional to its displacement from equilibrium. As the pendulum swings back and forth, it follows a sinusoidal pattern, with the maximum displacement at the bottom of the swing and the minimum displacement at the top.

3. What is the relationship between the period of a pendulum and its length?

The period (time for one complete back and forth swing) of a pendulum is directly proportional to the square root of its length. This means that a longer pendulum will have a longer period, while a shorter pendulum will have a shorter period.

4. How does increasing the mass of a pendulum affect its motion?

Increasing the mass of a pendulum does not affect its motion, as long as the length and amplitude (maximum displacement) remain constant. This is because the period of a pendulum is only dependent on its length and not its mass.

5. What other factors can affect the motion of a pendulum?

The motion of a pendulum can also be affected by air resistance, friction, and the angle at which it is released. These factors can cause the pendulum to deviate from simple harmonic motion and affect its period and amplitude.

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