Can someone check my logic? simple harmonic motion.

In summary, the discussion was about whether the daily movement of a student from home to school and back can be considered simple harmonic motion. It was concluded that this type of movement is not simple harmonic, as it is linear and does not follow a sinusoidal wave pattern. Instead, it falls into the category of complex harmonic motion.
  • #1
aliciagu
7
0

Homework Statement



Is the daily movement of a student from home to school and back simple harmonic motion?

Homework Equations





The Attempt at a Solution



I don't think it is. This type of movement is linear. It involves distance, speed and so on. It does not follow a sinusoidal wave pattern, either because though it is periodic, it's not regular. Does that make sense? Can someone else perhaps explain it better?
 
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  • #2
Simple Harmonic motion is defind by the following differential equation:

[tex]m/frac{d^2x}{dt^2}=-kx[/tex]

The solution to this equation is a sinusoidal function. As you said, the motion of the student is periodic, but not sinusoidal.

I agree with you. The student's motion corresponds to a square wave (graph his displacement vs. time) This is not simple harmonic motion, but instead falls into the realm of complex harmonic motion.
 
  • #3


Your reasoning is correct. Simple harmonic motion is defined as a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and the motion follows a sinusoidal wave pattern. In the case of a student's daily movement, the restoring force is not directly proportional to the displacement and the motion does not follow a sinusoidal pattern. Therefore, it is not considered simple harmonic motion.
 

Related to Can someone check my logic? simple harmonic motion.

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, with a restoring force that is directly proportional to the displacement from the equilibrium position.

2. How can I determine if my logic for simple harmonic motion is correct?

To check your logic for simple harmonic motion, you can use mathematical equations such as Hooke's law and the equation for simple harmonic motion to verify that your calculations are correct. Additionally, you can also use diagrams or simulations to visualize the motion and make sure it aligns with your logic.

3. What are the key factors that affect simple harmonic motion?

The key factors that affect simple harmonic motion are the mass of the object, the spring constant of the spring, and the amplitude and frequency of the oscillation. These factors determine the period and frequency of the motion.

4. Can simple harmonic motion occur in other systems besides a mass-spring system?

Yes, simple harmonic motion can occur in other systems as well, such as a pendulum, a swinging door, or an oscillating circuit. These systems have different restoring forces, but they still exhibit the same type of periodic motion.

5. How is simple harmonic motion useful in real-life applications?

Simple harmonic motion has many practical applications, such as in clock mechanisms, musical instruments, and shock absorbers. It is also used in scientific research, such as studying the motion of molecules and atoms.

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