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.
![### Problem Statement
1. A fisherman's spring scale stretches 3.9 cm when a 2.7 kg fish hangs from it.
- **(A)** What is the spring constant of the scale?
### Diagram and Explanation
**Explanation**: When a mass is hung from a spring scale, the force due to the weight of the mass causes the spring to stretch. The relationship between the force, spring constant, and displacement is given by Hooke's Law:
\[ F = k \cdot x \]
where:
- \( F \) is the force exerted by the weight of the fish,
- \( k \) is the spring constant,
- \( x \) is the displacement of the spring.
**Given Values**:
- Mass of the fish, \( m = 2.7 \, \text{kg} \)
- Displacement of the spring, \( x = 3.9 \, \text{cm} = 0.039 \, \text{m} \)
Since the force \( F \) is caused by the weight of the fish, we can calculate it using:
\[ F = m \cdot g \]
where \( g \approx 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.
### Calculation
1. Calculate the force exerted by the fish:
\[
F = 2.7 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 26.46 \, \text{N}
\]
2. Using Hooke's Law to find the spring constant \( k \):
\[
26.46 \, \text{N} = k \times 0.039 \, \text{m}
\]
\[
k = \frac{26.46 \, \text{N}}{0.039 \, \text{m}} = 678.46 \, \text{N/m}
\]
**Answer**: The spring constant of the scale is approximately \( 678.46 \, \text{N/m} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24666b77-75da-49bd-bf84-8c4674dedd2c%2F6c5a7148-8859-413a-af70-c03949c2c118%2Fcntn9q.png&w=3840&q=75)
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