An object moves in simple harmonic motion with amplitude 13cm and period 0.25 seconds. At time t=0 seconds, its displacement d from rest is 0cm, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time t. d=◻

Equation for Simple Harmonic Motion: The general form of the equation for simple harmonic motion is d(t) = A * sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase shift.Given Amplitude: The amplitude A is given as 13 cm, so A = 13.Calculate Angular Frequency: The period T is given as 0.25 seconds. The angular frequency ω is related to the period by the formula ω = 2π/T.Calculate Phase Shift: Calculate the angular frequency: ω = 2π/0.25 = 8π.Plug Values into Equation: Since the object starts at rest and moves in a positive direction at t=0, the phase shift φ is 0.Simplify Equation: Plug the values of A, ω, and φ into the general equation: d(t) = 13 * sin(8πt + 0).Simplify the equation: d(t) = 13 * sin(8πt).

Home

Math Problems

Grade 6

One-step inequalities: word problems

Full solution

Q. An object moves in simple harmonic motion with amplitude

13\,\text{cm}

and period

0.25\,\text{seconds}

. At time

t=0\,\text{seconds}

, its displacement

d

from rest is

0\,\text{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=

\square

Equation for Simple Harmonic Motion: The general form of the equation for simple harmonic motion is $d(t) = A \cdot \sin(\omega t + \varphi)$ , where $A$ is the amplitude, $\omega$ is the angular frequency, and $\varphi$ is the phase shift.
Given Amplitude: The amplitude $A$ is given as $13$ cm, so $A = 13$ .
Calculate Angular Frequency: The period $T$ is given as $0.25$ seconds. The angular frequency $\omega$ is related to the period by the formula $\omega = \frac{2\pi}{T}$ .
Calculate Phase Shift: Calculate the angular frequency: $\omega = \frac{2\pi}{0.25} = 8\pi$ .
Plug Values into Equation: Since the object starts at rest and moves in a positive direction at $t=0$ , the phase shift $\varphi$ is $0$ .
Simplify Equation: Plug the values of $A$ , $\omega$ , and $\varphi$ into the general equation: $d(t) = 13 \times \sin(8\pi t + 0)$ .
Simplify Equation: Plug the values of $A$ , $\omega$ , and $\varphi$ into the general equation: $d(t) = 13 \times \sin(8\pi t + 0)$ .Simplify the equation: $d(t) = 13 \times \sin(8\pi t)$ .