Respuesta :
Answer:
The equation of simple harmonic motion is [tex]y=5\sin{(8\pi t)}[/tex]
Explanation:
Given that,
Amplitude = 5 inches
Frequency [tex]f= \dfrac{4}{3}[/tex]
As per the question initial displacement is zero at t = 0 for sine curve.
The displacement is zero so the phase difference will be zero.
We know that,
The general equation of simple harmonic motion
[tex]y=A\sin(\omega t+\phi)[/tex]
Where, A = amplitude
[tex]\omega[/tex] = angular frequency
[tex]\phi[/tex] = phase shift
We need to calculate the time period
Using formula of frequency
[tex]f=\dfrac{1}{T}[/tex]
[tex]T=\dfrac{1}{f}[/tex]
Put the value into the formula
[tex]T=\dfrac{1}{\dfrac{4}{3}}[/tex]
[tex]T=\dfrac{3}{4}[/tex]
We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega=\dfrac{2\pi}{T}[/tex]
[tex]\omega=\dfrac{2\pi\times4}{3}[/tex]
Put the value into the general equation
[tex]y=5\sin{(8\pi t)}[/tex]
Hence, The equation of simple harmonic motion is [tex]y=5\sin{(8\pi t)}[/tex]
