Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion
Simple Harmonic Motion (SHM) describes the oscillatory motion of an object where the restoring force is directly proportional to the displacement from its equilibrium position. In this context, the shaking of the automobile can be modeled as SHM, where the imbalance in the tire creates a periodic force that leads to oscillations at specific frequencies.
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Natural Frequency
Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving force. For the automobile, the natural frequency of the wheel system can be determined by its mass and the spring constant, which influences the speed at which the shaking occurs. This frequency is critical for identifying the speed at which resonance may amplify the shaking.
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Resonance
Resonance occurs when an external force drives a system at its natural frequency, resulting in increased amplitude of oscillation. In the case of the automobile, if the speed of the car matches the natural frequency of the shaking caused by the unbalanced tire, resonance will occur, leading to significant vibrations. Understanding this concept is essential for determining the specific speed at which the wheel will shake most.
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