Why Does Acceleration Decrease When Velocity Increases in SHM?

In summary, when a mass is in SHM and moving towards equilibrium point, its velocity increases while its acceleration decreases. The gradient of velocity is positive when it is increasing and zero when it reaches its maximum at the equilibrium point. A link to a graph of position, velocity, and acceleration in SHM is provided, along with an explanation of the equation for position versus time and how to differentiate it to get velocity and acceleration. The concept of derivatives of sinusoidal functions is also discussed. Finally, it is mentioned that calculus is necessary to fully understand the relationship between velocity and acceleration in SHM.
  • #1
Josielle Abdilla
50
4
When a mass is in SHM, and is moving towards equilibrium point, its velocity starts to increase but why does acceleration decreases? What is the gradient when velocity is increasing and when it is at maximum? Thanks a lot!
 
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  • #2
Can you find a plot of the position, velocity and acceleration of a mass in SHM and provide a link? Are you familiar with the equation for the position of the mass versus time, and how to differentiate it to get the velocity and acceleration? :smile:
 
  • #3
I am only familiar with the displacement,velocity, and acceleration time graphs but I don't understand them quite well. The diagram attached shows the simple pendulum I am referring to
 

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  • #4
Here is the graph I was referring to below...

Are you familiar with derivatives of sinusoidal functions?

http://www.physics.usyd.edu.au/teach_res/jp/waves/hwaves100506_files/image008.gif

image008.gif
 

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  • #5
Yea, I am familiar with these sinusoidal graphs but i still don't know why acceleration decreases while velocity increases although I understand as to why acceleration increases as velocity decreases due to the increase in the retarding force
 
  • #6
Josielle Abdilla said:
Yea, I am familiar with these sinusoidal graphs but i still don't know why acceleration decreases while velocity increases although I understand as to why acceleration increases as velocity decreases due to the increase in the retarding force
Furthermore, I also struggle in trying to understand the equation of x=asin(wt) but this can be because i don't study maths at advanced level
 
  • #7
The velocity (actually the speed or the magnitude of velocity) decreases when the acceleration is negative. Nothing to do with the fact that the acceleration is increasing or decreasing. It could be constant negative acceleration and the velocity will decrease too.

The relation between velocity and acceleration is the same for any system: velocity is the first derivative of acceleration in respect to time. Positive acceleartion means that the velocity increases and negative acceleration means that velocity decreases.
 
  • #8
Josielle Abdilla said:
When a mass is in SHM, and is moving towards equilibrium point, its velocity starts to increase but why does acceleration decreases? What is the gradient when velocity is increasing and when it is at maximum? Thanks a lot!

In SHM when a mass moves towards equilibrium position, by definition it is restoring itself to a neutral position. Hence, at equilibrium position the force acting on it would be zero (since if it still had force acting on it, it would not be called a neutral or equilibrium position). But while coming back to the neutral position it gains a lot of momentum or velocity on account of force that is continuously accelerating it and therefore increasing the velocity till it maxes at equilibrium position since at this point the force acting is zero. And on account of Newton's 1st law of motion, it continues to swing to the other end.
 
  • #9
Josielle Abdilla said:
i still don't know why acceleration decreases while velocity increases

Do you know any calculus, specifically differential calculus and the derivatives of sine and cosine functions?
 

1. Why does acceleration decrease when velocity increases in SHM?

In simple harmonic motion (SHM), the acceleration is directly proportional to the displacement from equilibrium and is in the opposite direction. As the object moves away from equilibrium, the acceleration decreases because the force acting on it decreases. When the object reaches the maximum displacement, the acceleration becomes zero because the force is also zero at that point. As the object moves back towards equilibrium, the acceleration increases again in the opposite direction.

2. How is SHM related to acceleration and velocity?

In SHM, the acceleration and velocity are directly related to each other. The acceleration is proportional to the displacement from equilibrium and is in the opposite direction, while the velocity is proportional to the displacement and is in the same direction. This means that as the object moves away from equilibrium, the acceleration decreases while the velocity increases. As the object moves towards equilibrium, the acceleration increases while the velocity decreases.

3. Does the acceleration always decrease when the velocity increases in SHM?

Yes, in SHM, the acceleration always decreases when the velocity increases. This is because of the relationship between acceleration and displacement, as well as the fact that the force acting on the object is proportional to the displacement. As the object moves away from equilibrium, the force and acceleration decrease, leading to an increase in velocity. As the object moves towards equilibrium, the force and acceleration increase, causing a decrease in velocity.

4. How does the amplitude affect the relationship between acceleration and velocity in SHM?

The amplitude, or maximum displacement, does not affect the relationship between acceleration and velocity in SHM. The relationship remains the same regardless of the amplitude. However, the amplitude does affect the maximum values of acceleration and velocity. A larger amplitude will result in a larger maximum acceleration and velocity, while a smaller amplitude will result in smaller maximum values for acceleration and velocity.

5. Can the acceleration and velocity ever be in the same direction in SHM?

No, the acceleration and velocity can never be in the same direction in SHM. This is because the acceleration is always in the opposite direction of the displacement, while the velocity is always in the same direction as the displacement. Therefore, as the displacement increases, the velocity also increases, but the acceleration decreases. As the displacement decreases, the velocity also decreases, but the acceleration increases. This relationship ensures that the acceleration and velocity are always in opposite directions.

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