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Import favorites $\newline$ MVNU Students Ho... $\newline$ A $\newline$ ALEKS - Jameson C... $\newline$ Trigonometric Graphs $\newline$ Word problem involving a sine or cosine function: Problem type $1$ $\newline$ Jameson $\newline$ Español $\newline$ An object moves in simple harmonic motion with amplitude $13 \mathrm{~cm}$ and period $0$ . $25$ seconds. At time $t=0$ seconds, its displacement $d$ from rest is $0 \mathrm{~cm}$ , and initially it moves in a positive direction. $\newline$ Give the equation modeling the displacement $d$ as a function of time $t$ . $\newline$ $d=$ $\newline$ $\square$ $\newline$ $\square$ $\newline$ Explanation $\newline$ Check $\newline$ (C) $2024$ McGraw Hill LLC. All Rights Reserved. $\newline$ Terms of Use $\newline$ Privacy Center $\newline$ Accessibility $\newline$ Type here to search $\newline$ $59^{\circ} \mathrm{F}$ $\newline$ ( $1$ )) $\newline$ $2$ : $11$ PM $\newline$ $4 / 22 / 2024$

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Q. Import favorites

\newline

MVNU Students Ho...

\newline

\newline

ALEKS - Jameson C...

\newline

Trigonometric Graphs

\newline

Word problem involving a sine or cosine function: Problem type

1

\newline

Jameson

\newline

Español

\newline

An object moves in simple harmonic motion with amplitude

13 \mathrm{~cm}

and period

0

25

seconds. At time

t=0

seconds, its displacement

d

from rest is

0 \mathrm{~cm}

, and initially it moves in a positive direction.

\newline

Give the equation modeling the displacement

d

as a function of time

t

\newline

d=

\newline

\square

\newline

\square

\newline

Explanation

\newline

Check

\newline

(C)

2024

\newline

\newline

Privacy Center

\newline

Accessibility

\newline

Type here to search

\newline

59^{\circ} \mathrm{F}

\newline

(

1

))

\newline

2

11

\newline

4 / 22 / 2024

Identify Amplitude and Period: Identify the amplitude ( $A$ ) and period ( $T$ ) of the simple harmonic motion. The amplitude is $13\,\text{cm}$ and the period is $0.25\,\text{seconds}$ .
Recall General Equation: Recall the general form of the equation for simple harmonic motion, which is $d(t) = A \cdot \sin(2\pi \cdot t / T + \varphi)$ , where $\varphi$ is the phase shift.
Determine Phase Shift: Since the object starts at rest and moves in a positive direction at $t=0$ , the phase shift $\varphi$ is $\frac{\pi}{2}$ radians.
Substitute Values: Substitute the values of $A$ , $T$ , and $\varphi$ into the equation. $d(t) = 13 \times \sin(2\pi \times t / 0.25 + \pi/2)$ .
Simplify Equation: Simplify the equation by calculating the coefficient of $t$ inside the sine function. The coefficient is $\frac{2\pi}{0.25} = 8\pi$ .
Write Final Displacement Function: Write the final equation for the displacement $d$ as a function of time $t$ . $d(t) = 13 \cdot \sin(8\pi \cdot t + \frac{\pi}{2})$ .