he graph shows the force F that an archer applies to the string of a long bow versus the string's displacement x. Drawing back this bow is analogous to stretching a spring. If Fmax = 153 N and xmax = 0.21 m, determine the effective spring constant of the bo
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
The graph shows the force F that an archer applies to the string of a long bow versus the string's displacement x. Drawing back this bow is analogous to stretching a spring. If Fmax = 153 N and xmax = 0.21 m, determine the effective spring constant of the bow.
N/m
![### Understanding Force-Displacement Graphs
#### Description of the Graph
The graph provided is a Force-Displacement (F-x) graph. Here are the key elements and details of the graph:
1. **Axes:**
- The vertical axis is labeled as \( F \) (N), denoting force measured in Newtons.
- The horizontal axis is labeled as \( x \) (m), denoting displacement measured in meters.
2. **Variables:**
- Along the vertical axis, \( f_{max} \) is indicated at the upper end, representing the maximum force.
- Along the horizontal axis, \( i_{max} \) is indicated at the far right end, representing the maximum displacement.
3. **Graph Line:**
- A red line starts from the origin (0,0) and extends to the top right corner of the graph, indicating a linear relationship between force and displacement.
- The line suggests that as displacement increases, the force increases proportionally, which signifies a region of linear elastic behavior according to Hooke's Law.
### Interpretation
This graph typically represents the elastic region of a material where the force applied is directly proportional to the displacement in accordance with Hooke's Law, which states:
\[ F = kx \]
Where \( F \) is the force applied to the material, \( x \) is the displacement, and \( k \) is the stiffness (or spring constant) of the material.
### Educational Insights
1. **Linear Relationship:**
The straight line on the graph indicates a linear relationship between force and displacement. In this region, the material returns to its original shape after the force is removed.
2. **Maximum Values:**
The \( f_{max} \) and \( i_{max} \) represent the maximum limits of force and displacement respectively before the material potentially undergoes plastic deformation, where it may not return to its original shape.
3. **Applications:**
Understanding this graph is crucial in fields such as material science and mechanical engineering for designing structures and selecting materials that can withstand specified loads without permanent deformation.
#### Conclusion
This Force-Displacement graph is a fundamental concept for understanding material behavior under load, critical for designing safe and efficient structures and mechanical systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc09f92c9-f87d-47bc-8050-c41fc7667ccc%2Fccf7349d-f337-4682-8e33-dfac63652131%2Fnifcyeh_processed.gif&w=3840&q=75)
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