A machine part is undergoing SHM with a frequency of 4.00 Hz and amplitude 1.80 cm. How long does it take the part to go from x = 0 to x = -1.80 cm ?

검증된 단계별 안내

Start by understanding the concept of Simple Harmonic Motion (SHM). SHM is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

Identify the given parameters: frequency (f) = 4.00 Hz and amplitude (A) = 1.80 cm. The displacement we are interested in is from x = 0 to x = -1.80 cm.

Use the formula for the period of SHM, which is the reciprocal of frequency: \( T = \frac{1}{f} \). Calculate the period using the given frequency.

The displacement in SHM can be described by the equation \( x(t) = A \cos(\omega t + \phi) \), where \( \omega = 2\pi f \) is the angular frequency. Since the motion starts from x = 0, the phase angle \( \phi \) is \( \frac{\pi}{2} \).

Determine the time it takes to reach x = -1.80 cm by solving the equation \( x(t) = A \cos(\omega t + \phi) \) for t, using the known values of A, \( \omega \), and \( \phi \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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 back and forth through an equilibrium position. The motion is characterized by a restoring force proportional to the displacement, often described by sine or cosine functions. Understanding SHM is crucial for analyzing the motion of the machine part in the problem.

Frequency and Period of SHM

Frequency, measured in Hertz (Hz), is the number of oscillations per second in SHM. The period is the time taken for one complete cycle of motion and is the inverse of frequency. In this problem, the frequency is given as 4.00 Hz, which helps determine the period and subsequently the time taken for specific displacements.

Phase and Displacement in SHM

In SHM, the phase determines the position and direction of motion at any given time. The displacement is the distance from the equilibrium position. For this problem, understanding how the phase relates to displacement allows us to calculate the time taken for the part to move from x = 0 to x = -1.80 cm, considering the amplitude and frequency.