The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (c) the period? (d) the angular frequency of this motion?

검증된 단계별 안내

To find the amplitude, observe the maximum displacement from the equilibrium position on the graph. The amplitude is the absolute value of this maximum displacement.

To determine the period, identify the time it takes for the oscillating object to complete one full cycle. This can be found by measuring the time interval between two consecutive points where the object is at the same position and moving in the same direction.

The frequency is the reciprocal of the period. Use the formula: \( f = \frac{1}{T} \), where \( f \) is the frequency and \( T \) is the period.

The angular frequency can be calculated using the formula: \( \omega = 2\pi f \), where \( \omega \) is the angular frequency and \( f \) is the frequency.

Review the graph to ensure that the measurements for amplitude, period, and frequency are consistent with the visual data, and adjust if necessary.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Period

The period of an oscillating object is the time it takes to complete one full cycle of motion. In the context of simple harmonic motion, it is the duration between successive peaks or troughs in the displacement graph. From the provided graph, the period can be determined by measuring the time interval between two consecutive maximum or minimum points.

Angular Frequency

Angular frequency, denoted by the symbol ω, is a measure of how quickly an object oscillates in radians per second. It is related to the period (T) by the formula ω = 2π/T. This concept is crucial for understanding the dynamics of oscillatory motion, as it provides insight into the speed of oscillation in relation to the circular motion analogy.

Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium position and acts in the opposite direction. This motion can be represented graphically as a sine or cosine wave, as seen in the displacement vs. time graph. Understanding SHM is essential for analyzing the behavior of oscillating systems, such as springs and pendulums.