Question

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 10 cos 2πt

Accepted Answer

Identify the given equation of simple harmonic motion: $$d = 10 \cos 2\pi t$$, where $$d is $$displacement and $$t is $$time in seconds. To find the maximum displacement, recognize that the amplitude of the motion is the coefficient in front of the cosine function. So, the maximum displacement is the absolute value of 10. To find the frequency, recall that the general form of simple harmonic motion is $$d = A \cos(\omega t)$$, where $$\omega is $$the angular frequency in radians per second. Here, $$\omega = 2\pi. $$Use the relation $$f = \frac{\omega}{2\pi} to $$find the frequency. To find the time required for one cycle (the period), use the formula $$T = \frac{1}{f}$$, where $$T is $$the period and $$f is $$the frequency found in the previous step. Summarize the results: maximum displacement is the amplitude, frequency is calculated from angular frequency, and period is the reciprocal of frequency.

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 10 cos 2πt

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Simple Harmonic Motion (SHM)

Amplitude and Maximum Displacement

Frequency and Period of Oscillation