Answer:
, where t is measure in minutes.
Step-by-step explanation:
The statement consists in the construction of the motion function for a object experimenting a simple harmonic motion. The expression for simple harmonic motion is:
![x(t) = A\cdot \cos (\omega\cdot t + \phi)](https://tex.z-dn.net/?f=x%28t%29%20%3D%20A%5Ccdot%20%5Ccos%20%28%5Comega%5Ccdot%20t%20%2B%20%5Cphi%29)
Where:
- Amplitude, in m.
- Angular frequency, in rad/s.
- Phase angle, in rad.
The angular frequency is:
![\omega = \frac{2\pi}{T}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BT%7D)
![\omega = \frac{2\pi}{180\,s}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B180%5C%2Cs%7D)
![\omega = \frac{\pi}{90}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B%5Cpi%7D%7B90%7D)
The amplitude of the motion is 13 m and the phase angle is:
![(13\,m)\cdot \cos \phi = -13\,m](https://tex.z-dn.net/?f=%2813%5C%2Cm%29%5Ccdot%20%5Ccos%20%5Cphi%20%3D%20-13%5C%2Cm)
![\cos \phi = -1](https://tex.z-dn.net/?f=%5Ccos%20%5Cphi%20%3D%20-1)
![\phi = \pm\pi](https://tex.z-dn.net/?f=%5Cphi%20%3D%20%5Cpm%5Cpi)
The position function for the object is:
, where t is measure in minutes.