A 22 kq object is mass is pulled 0.35m downward from its equilibrium position and allowed to oscillate. What is the maxium Kinetic enerau or the Suspended from a spring with k=18 Nim. The Object?
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
A 2.2 kg object is suspended from a spring with k = 18 N/m. The mass is pulled 0.35 m downward from its equilibrium position and allowed to oscillate. What is the maximum kinetic energy of the object?
### Explanation:
In this scenario, we can determine the maximum kinetic energy of the object using the law of conservation of energy. When the object is at its maximum displacement (0.35 m), the entire energy of the system is in the form of elastic potential energy stored in the spring. As the object passes through the equilibrium position, this potential energy is converted into kinetic energy.
The elastic potential energy (U) in a spring is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
where:
- \( k \) is the spring constant (18 N/m),
- \( x \) is the displacement from equilibrium (0.35 m).
Plugging in these values:
\[ U = \frac{1}{2} \times 18 \, \text{N/m} \times (0.35 \, \text{m})^2 \]
\[ U = \frac{1}{2} \times 18 \times 0.1225 \]
\[ U = 1.1025 \, \text{J} \]
Therefore, the maximum kinetic energy of the object is 1.1025 Joules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faea29e6a-b699-42f9-bc31-a2ac588bd4f7%2F247d3719-78cd-44ad-b599-36340672e0e2%2Fq4drve8_processed.jpeg&w=3840&q=75)
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