This figure shows on the position versus time graph for a 9.8 kg object oscillating on a spring. Assume that each take mark on the vertical axis represents 7 cm and assume each take more on the horizontal axis represents 10 seconds what is the frequency in hertz of the motion.
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.
![### Position vs. Time Graph
#### Description
This graph displays the relationship between position (x) in meters and time (t) in seconds for a given motion.
#### Axes:
- **Horizontal Axis (x-axis)**: Represents time in seconds (s).
- **Vertical Axis (y-axis)**: Represents position in meters (m).
#### Graph Characteristics:
- The graph displays a sinusoidal wave pattern, indicating harmonic or oscillatory motion.
- Starting from the initial point on the vertical axis, the position decreases, reaching a minimum, then increases, passes through the initial position, reaches a maximum, and finally returns toward the initial position again.
- The smooth, continuous curve suggests regular periodic motion.
#### Interpreting the Graph:
- **Peak Points**: Points where the curve reaches the maximum and minimum values signify the extreme positions of the oscillatory motion.
- **Zero Crossings**: Points where the curve crosses the horizontal axis correspond to the moments when the object passes through its equilibrium position.
- **Periodicity**: The distance along the time axis between two successive points where the curve starts repeating indicates the period of the oscillatory motion.
This graph is typical in studies of physics related to waves, simple harmonic motion, and oscillatory systems. It helps in understanding how an object's position varies over time following these principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdce31da-09da-4c4c-8ce9-9517d7b65c94%2F01fa399a-ae97-451f-972f-ccb74f2f75f8%2F9lafzza_processed.jpeg&w=3840&q=75)
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