Goals
1. Comprehend that Simple Harmonic Motion (SHM) refers to a type of motion where the acceleration of an object is directly proportional but opposite to its displacement from a central point.
2. Experimentally determine whether a body is experiencing SHM.
Contextualization
Simple Harmonic Motion (SHM) is a foundational concept in physics, evident in many situations we encounter daily, like the swinging of pendulums, the stretching of springs, and the behaviour of certain electronic devices. Grasping SHM not only sheds light on these scenarios but also enables us to apply this knowledge in fields such as engineering, robotics, and sensor technology. For instance, SHM is vital for the functioning of pendulum clocks and plays a role in the development of shock absorbers and car suspension systems, enhancing both comfort and safety.
Subject Relevance
To Remember!
Definition of Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM) is a kind of periodic motion where an object's acceleration is directly proportional to its displacement from a resting point, but in the opposite direction. In essence, the object oscillates around a balance point, being pulled back by a restoring force whenever it strays away.
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Acceleration is directly proportional to displacement.
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The direction of acceleration goes against the displacement.
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The motion is periodic, repeating at consistent intervals.
Equation of Simple Harmonic Motion
The equation that defines Simple Harmonic Motion is expressed as F = -kx, wherein F represents the restoring force, k is the spring constant (or proportionality constant), and x symbolizes the displacement from the rest position. This formula is derived from Newton's second law and the concept of restoring force.
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F = -kx illustrates the relationship between restoring force and displacement.
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k indicates the spring constant or proportionality factor.
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x denotes the object's displacement from its equilibrium position.
Characteristics of Simple Harmonic Motion
SHM possesses specific traits like period, frequency, and amplitude. The period refers to the duration it takes for the object to complete one full oscillation. Frequency indicates the number of oscillations occurring in one second, while amplitude signifies the farthest distance from the central position.
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Period (T) is the time for one complete oscillation.
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Frequency (f) is the number of oscillations per second.
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Amplitude (A) is the maximum distance from the rest point.
Practical Applications
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Pendulum clocks: Utilise SHM to keep accurate time.
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Car suspension systems: Implement SHM principles to improve vehicle comfort and safety.
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Precision sensors: Accelerometers in smartphones harness SHM to measure accelerations with high precision.
Key Terms
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Simple Harmonic Motion (SHM): Periodic motion where acceleration is proportional and opposite to the displacement.
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Period (T): Time taken for one complete oscillation.
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Frequency (f): Number of oscillations each second.
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Amplitude (A): Maximum distance from the rest point.
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Restoring force (F): Force that brings the object back to its balance point.
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Spring constant (k): Relationship between restoring force and displacement.
Questions for Reflections
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How can understanding SHM aid in enhancing automotive suspension systems?
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What other technologies, besides accelerometers, incorporate SHM principles?
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In what ways can knowledge of SHM influence the creation of new technologies within engineering and robotics?
Practical Challenge: Verification of Simple Harmonic Motion
In this mini-challenge, you will assemble a basic pendulum and experimentally confirm the characteristics of Simple Harmonic Motion (SHM).
Instructions
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Form groups of 3-4 learners.
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Collect the necessary items: string, weight (small metal ball or known weight), ruler, stopwatch, and a support to suspend the pendulum.
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Create the pendulum by securing one end of the string to the support and the other end to the weight.
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Measure the length of the string and record your findings.
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Displace the weight from its balance position and let it go, initiating the pendulum's swing.
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Use the stopwatch to time 10 complete swings and compute the average period of the pendulum.
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Determine the frequency based on the average period.
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Verify the correlation between the period and string length via the pendulum's period formula.
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Discuss whether the observed motion represents SHM and justify your reasoning using the collected data.
