Respuesta :
The motion of the mass as it moves on the bottom of the spring is a
repetitive motion.
- [tex]\mathrm{The \ motion \ of \ the \ mass \ attached \ to \ the \ spring \ is \ }\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]
Reasons:
The general form of the equation of the simple harmonic motion of the
mass is d = a·sin(ω·t)
Where;
d = The distance of the mass from the rest position
a = The maximum displacement of the mass from the equilibrium position = 6 cm
ω = The frequency of rotation
t = The time of motion
ω = The frequency of rotation
[tex]\displaystyle \omega = \mathbf{\frac{2 \cdot \pi}{T}}[/tex]
Where;
T = The time to complete one cycle (the period of oscillation) = 4 seconds
[tex]\displaystyle \omega = \frac{2 \cdot \pi}{4} = \frac{\pi}{2}[/tex]
Combining the above values gives the modelling equation as follows;
[tex]\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]
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