last question: pleaseee help :/

The displacement of a mass suspended on a spring is modeled by the function y = 3sin(4)(pi)(t), where y is measured in inches and t in seconds. The amplitude, period, and frequency of the motion of the mass are given by

Aamplitude = 2, period = 2, and frequency =
Bamplitude = 4, period = 2, and frequency = 1
Camplitude = 3, period = , and frequency = 4
Damplitude = 3, period = , and frequency = 2

I believe the correct answer from the choices listed above is option D. The amplitude, period, and frequency of the motion of the mass are given by amplitude = 3, period = , and frequency = 2. The standard form of this model would be as follows:

y = A sin Bx

where A is the amplitude and 2pi/B is the period. Frequency is the reciprocal of the period. Hope this answers the question. Have a nice day.

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lidaralbany lidaralbany · Answer 2 · 2019-05-16T04:30:25-04:00

Answer:

The amplitude is 3, the time period is 0.5 and the frequency is 2.

D is correct.

Explanation:

Given that,

\(y = 3 sin(4)(\pi)(t)\)

We know that,

The general equation of the S.H.M

\(y = A\ sin\omega\ t\)

Where, y = displacement

A = amplitude

According to equation,

Amplitude = 3

The frequency is

Frequency \(\omega = 2\pi f\)

\(4\pi=2\pi f\)

\(f = 2\)

The time period is reciprocal of frequency.

\(T = \dfrac{1}{f}\)

\(T =\dfrac{1}{2}\)

\(T = 0.5\)

Hence, The amplitude is 3, the time period is 0.5 and the frequency is 2.