Respuesta :
Answer:
The equation of motion is [tex]y(t)=22sin(\frac{2\pi }{3}t)[/tex]
Explanation:
The general equation of motion of a SHM motion is given by
[tex]y(t)=Asin(\omega t+\phi )[/tex]
where,
A is the amplitude of the motion
ω is the natural frequency of the system
Since amplitude is defines as the maximum displacement of the object from the mean position we have
[tex]2A=85 cm-41 cm\\\\A=\frac{44}{2}cm\\\\\therefore A=22cm[/tex]
Now the time period is related to the natural angular frequency as
[tex]\omega =\frac{2\pi }{T}\\\\\therefore \omega=\frac{2\pi }{3}[/tex]
Thus the equation of motion becomes
[tex]y(t)=22sin(\frac{2\pi }{3}t+\phi )[/tex]
the initial phase can be assumed to be zero thus the equation becomes
[tex]y(t)=22sin(\frac{2\pi }{3}t)[/tex]
Answer:
Using equation
y(t)=y0*Cos(wt)
w=2[tex]\pi[/tex]/3
y0=85-41
y(t)=44cos(2[tex]\pi[/tex]/3*t)
