The y-position of a damped oscillator as a function of time is shown in the figure. y (cm) 5 4 3 2 O H N -3 -4 -5 H 0 1 7 t(s) This function can be described by the y(t) = Ae¯-btcos(wt) formula, where A is the initial amplitude, b is the damping coefficient and w is the angular frequency. 2 3 Submit An 4 5 6 Incorrect. 8 9 10 What is the period of the oscillator? Please, notice that the function goes through a grid intersection point. 1.22 s 11 12 13 14 15 Determine the damping coefficient. 0.063 S-1 Submit Answer -Unable to interpret units. Computer reads units as "S-1". Previous Tries 0/12 Tries
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 y-position of a damped oscillator as a function of time is shown in the figure.
**Graph Explanation:**
The graph depicts the y-position (in cm) of a damped oscillator over time (in seconds). The waveform exhibits an oscillatory motion with decreasing amplitude, indicative of a damped oscillation.
**Key Points:**
- The x-axis represents time \( t \) in seconds (s), ranging from 0 to 15 seconds.
- The y-axis represents the position \( y \) in centimeters (cm), ranging from -5 to 5 cm.
- The waveform shows a reduction in the peak heights over time due to damping.
- The graph shows distinct oscillations slowly approaching zero.
**Function Description:**
The motion of the oscillator can be modeled by the equation:
\[ y(t) = A_0 e^{-bt} \cos(\omega t) \]
where:
- \( A_0 \) is the initial amplitude.
- \( b \) is the damping coefficient.
- \( \omega \) is the angular frequency.
**Questions and Answers:**
1. **What is the period of the oscillator?**
*Notice that the function crosses a grid intersection point.*
- **Answer:** 1.22 s
- Note: An incorrect entry was previously provided.
2. **Determine the damping coefficient.**
- **Answer:** 0.063 s\(^{-1}\)
- Note: There was a unit interpretation error, read as "s\(^{-1}\)".
This analysis aids in understanding damped oscillations and their mathematical representation for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29d54699-8096-4754-af5c-5369115407dd%2Fd38002b4-3d37-4c3b-bad4-1fac9ffdd055%2F1bdrp9h_processed.png&w=3840&q=75)
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