Suppose that, for the graph shown below, each division on the time scale represents 2.50 x 10-3 s and divisions on the displacement scale are in 1 cm increments. MAR (a) Find the amplitude. (b) Find the period. (c) Find the frequency. (d) Find the displacement at t = 0.035 s Time
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.
#### Annotations:
- **Amplitude (A)**: The maximum displacement from the equilibrium position.
- **Period (T)**: The time taken for one complete cycle of the wave.
#### Questions:
1. **Find the amplitude.**
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2. **Find the period.**
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3. **Find the frequency.**
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4. **Find the displacement at \( t = 0.035 \, \text{s} \).**
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#### Detailed Explanations of the Graph:
- **Displacement vs. Time Graph**:
- The vertical axis represents displacement in centimeters.
- The horizontal axis represents time in seconds.
- The wave pattern provides both positive and negative displacements, indicating oscillatory motion (e.g., sine wave).
### Steps to Solve Each Question:
1. **Finding the Amplitude**:
- Identify the peak (maximum positive or negative displacement) value on the graph.
- Count the number of divisions from the equilibrium (center) line to the peak.
- Multiply the number of divisions by the displacement increment (1 cm).
2. **Finding the Period**:
- Identify one complete cycle (from one crest to the next crest or one trough to the next trough).
- Count the number of divisions representing one complete cycle.
- Multiply the number of divisions by the time increment (\(2.50 \times 10^{-3} \, \text{s}\)).
3. **Finding the Frequency**:
- Use the formula: \( \text{Frequency} (f) = \frac{1}{\text{Period} (T)} \).
4. **Finding the Displacement at \( t = 0.035 \, \text{s} \)**:
- Locate the specific time point (\(0.035 \, \text{s}\)) on the horizontal axis.
- Count the divisions to determine the position on the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb64acd3a-f42e-4e9c-a1af-15847420769a%2F223c8e4f-f3fa-473a-8ee3-99a96525b91b%2Fw25ugm8_processed.png&w=3840&q=75)
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