Find Amplitude and Equilibrium in Simple Harmonic Motion

In summary, we are given a particle undergoing simple harmonic motion with a mass of 0.241 kg and oscillating between the points x1 = -0.349 m and x2 = 0.419 m along the horizontal x-axis. The period of oscillation is 0.511 s. Using the hints provided, we can find the frequency, f, using the equation f = 1/T. To find the equilibrium position, xeq, we can use the midpoint formula (x1 + x2)/2. Finally, the amplitude, A, can be found using the distance between two points formula |x1 - x2|. By drawing the setup and considering the definitions and equations, we can determine these quantities.
  • #1
jcd2012
5
0

Homework Statement



A 0.241-kg particle undergoes simple harmonic motion along the horizontal x-axis between the points x1 = -0.349 m and x2 = 0.419 m. The period of oscillation is 0.511 s. Find the frequency, f, the equilibrium position, xeq, the amplitude, A.

Homework Equations



The hint system suggests:

Midpoint Formula: (X_1 + X_2)/2
Distance Between Two Points: |X_1 - X_2|

The Attempt at a Solution



I am just not sure how I get amplitude and equilibrium from this information. The hint system suggests that I draw the setup to determine these however I am lost from there.
 
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  • #2
I would suggest you consider the definitions and equations of frequency, equilibrium and amplitude. After drawing the system, consider how these quantities are represented in the system.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium and is directed towards the equilibrium position. In simpler terms, it is the back and forth motion of an object around a central point that is caused by a force that is directly proportional to its displacement.

2. How do I find the amplitude of a simple harmonic motion?

The amplitude of a simple harmonic motion is the maximum displacement from equilibrium. It can be found by measuring the distance from the equilibrium position to either the maximum or minimum point of the motion. Alternatively, it can also be calculated by dividing the range of motion (the distance between the maximum and minimum points) by 2.

3. What is the equilibrium position in simple harmonic motion?

The equilibrium position in simple harmonic motion is the point at which the net force on the object is zero, meaning there is no acceleration and the object is at rest. This is the central point around which the object oscillates back and forth.

4. How is equilibrium achieved in simple harmonic motion?

Equilibrium in simple harmonic motion is achieved when the restoring force (directed towards the equilibrium position) is equal in magnitude but opposite in direction to the displacement of the object. This creates a balanced system in which the object remains at rest at the equilibrium position.

5. Can the amplitude and equilibrium position in simple harmonic motion change over time?

Yes, the amplitude and equilibrium position in simple harmonic motion can change over time if there is an external force acting on the object. This can cause the equilibrium position to shift, and therefore change the amplitude of the motion. However, in ideal situations with no external forces, the amplitude and equilibrium position will remain constant throughout the motion.

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