Answer:
[tex]x=(0.088m)\cos(\sqrt{\frac{k}{m} } t)[/tex]
Explanation:
We first identify the elements of this simple harmonic motion:
The amplitude A is 8.8cm, because it's the maximum distance the mass can go away from the equilibrium point. In meters, it is equivalent to 0.088m.
The angular frequency ω can be calculated with the formula:
[tex]\omega =\sqrt{\frac{k}{m}}[/tex]
Where k is the spring constant and m is the mass of the particle.
Now, since the spring starts stretched at its maximum, the appropriate function to use is the positive cosine in the equation of simple harmonic motion:
[tex]x=A\cos(\omega t)[/tex]
Finally, the equation of the motion of the system is:
[tex]x=(0.088m)\cos(\omega t)[/tex]
or
[tex]x=(0.088m)\cos(\sqrt{\frac{k}{m} } t)[/tex]
