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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

A. amplitude = 2, period = 2, and frequency =
B. amplitude = 4, period = 2, and frequency = 1
C. amplitude = 3, period = , and frequency = 4
D. amplitude = 3, period = , and frequency = 2

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MissPhiladelphia
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.

Answer:

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

D is correct.

Explanation:

Given that,

[tex]y = 3 sin(4)(\pi)(t)[/tex]

We know that,

The general equation of the S.H.M

[tex]y = A\ sin\omega\ t[/tex]

Where, y = displacement

A = amplitude

According to equation,

Amplitude = 3

The frequency is

Frequency [tex]\omega = 2\pi f[/tex]

[tex]4\pi=2\pi f[/tex]

[tex]f = 2[/tex]

The time period is reciprocal of frequency.

[tex]T = \dfrac{1}{f}[/tex]

[tex]T =\dfrac{1}{2}[/tex]

[tex]T = 0.5[/tex]

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

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