A person stranded on a raft in the ocean Bobs up and down on ocean waves every three seconds. The unlucky person estimates that they rise and fall a total of about 6 meters. What is the amplitude of the bobbing of the raft?
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.
A person stranded on a raft in the ocean Bobs up and down on ocean waves every three seconds. The unlucky person estimates that they rise and fall a total of about 6 meters. What is the amplitude of the bobbing of the raft?
![**Wave Amplitude Problem**
**Question:**
11. A person stranded on a raft in the ocean bobs up and down on ocean waves every 3 seconds. The unlucky person estimates that they rise and fall a total of about 6 meters. What is the amplitude of the bobbing of the raft?
- A. 6 m
- B. 2 m
- C. 3 m
- D. 18 m
**Explanation:**
When considering wave motion, the amplitude is the measure from the resting position (equilibrium) to the peak of the wave. In this context, the total rise and fall of 6 meters represents the distance from the trough (lowest point) to the crest (highest point) of the wave.
Since the total motion is 6 meters, the amplitude (which is half the total distance) would be:
\[ \text{Amplitude} = \frac{\text{Total Distance}}{2} \]
\[ \text{Amplitude} = \frac{6 \text{ m}}{2} = 3 \text{ m} \]
Therefore, the correct answer is:
- C. 3 m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37797b3e-93b1-4c2c-98d5-fb6f936a5e8e%2F65dc9143-c09d-41f7-bed5-450184e975c5%2Fld6h5y_processed.jpeg&w=3840&q=75)
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