For the oscillating object in Fig. E14.4, what is its maximum acceleration?

검증된 단계별 안내

Identify the amplitude of the oscillation from the graph. The amplitude is the maximum displacement from the equilibrium position, which is 10 cm in this case.

Determine the angular frequency \( \omega \) of the oscillation. The period \( T \) can be found from the graph as the time it takes to complete one full cycle. From the graph, the period \( T \) is 10 seconds. Use the formula \( \omega = \frac{2\pi}{T} \) to calculate the angular frequency.

Recall the formula for maximum acceleration in simple harmonic motion: \( a_{max} = \omega^2 A \), where \( A \) is the amplitude and \( \omega \) is the angular frequency.

Substitute the values of \( \omega \) and \( A \) into the formula for maximum acceleration to find \( a_{max} \).

Ensure the units are consistent. Since the amplitude is given in cm, convert it to meters by dividing by 100 if necessary, to ensure the acceleration is in \( \text{m/s}^2 \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of periodic motion where an object oscillates around an equilibrium position. The motion is characterized by a restoring force proportional to the displacement from the equilibrium, leading to sinusoidal position, velocity, and acceleration graphs. In SHM, the maximum displacement from the equilibrium is known as the amplitude.

Acceleration in SHM

In Simple Harmonic Motion, the acceleration of the oscillating object is directly related to its displacement from the equilibrium position. The maximum acceleration occurs at the maximum displacement (amplitude) and is given by the formula a_max = ω²A, where ω is the angular frequency and A is the amplitude. This relationship highlights how acceleration varies throughout the oscillation.

Graph Interpretation

The graph provided depicts the position of the oscillating object over time, illustrating its periodic nature. By analyzing the graph, one can determine key parameters such as amplitude, period, and phase. The maximum displacement from the horizontal axis indicates the amplitude, while the steepest slopes correspond to maximum velocity, and the points of zero slope indicate maximum acceleration.