11) State the: midline, amplitude, period, horizontal shift, and phase shift. Then write a possible sine forn for the graph. Sçale Midline 2. AMP Amplitude = S 4 3 %3D Period = 2T Scaled shift = 5.5 units %3D
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.
![**Transcription and Explanation for Educational Use**
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**Problem Statement:**
11) State the: midline, amplitude, period, horizontal shift, and phase shift. Then write a possible sine form for the graph.
**Graph Analysis:**
- **Graph Description:** The graph shows a sinusoidal wave with annotations.
**Annotated Elements:**
1. **Midline:** A horizontal line drawn at y = 2. This indicates the central axis of the sinusoidal wave.
2. **Amplitude:** The distance from the midline to the peak of the wave, noted as 5 units.
3. **Period:** Shown as \(2\pi\), indicating the length of one complete cycle of the wave.
4. **Scaled Shift (Horizontal Shift):** The note indicates a shift of 5.5 units to the right.
5. **Other Annotations:**
- Scaled and labeled sections along the graph, indicating various measurements like amplitude and period.
**Calculated Values:**
- **Midline = 2**
- **Amplitude = 5**
- **Period = \(2\pi\)**
- **Scaled shift = 5.5 units**
**Phase Shift:**
- It is explicitly left blank in this graph.
**Possible Equation Form:**
The graph illustrates the function, with the equation given as:
\[ f(t) = 5 \sin(t - \]
(The phase shift part of the equation is left incomplete.)
**Conclusion:**
This graph represents a sine wave with the aforementioned attributes. Understanding these values helps in writing a function that describes the graph accurately.
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