Answer:
[tex]x(t) = (13\,m)\cdot \cos \left[\frac{2\pi}{3}\cdot t \pm \pi\right][/tex], 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:
[tex]x(t) = A\cdot \cos (\omega\cdot t + \phi)[/tex]
Where:
[tex]A[/tex] - Amplitude, in m.
[tex]\omega[/tex] - Angular frequency, in rad/s.
[tex]\phi[/tex] - Phase angle, in rad.
The angular frequency is:
[tex]\omega = \frac{2\pi}{T}[/tex]
[tex]\omega = \frac{2\pi}{180\,s}[/tex]
[tex]\omega = \frac{\pi}{90}[/tex]
The amplitude of the motion is 13 m and the phase angle is:
[tex](13\,m)\cdot \cos \phi = -13\,m[/tex]
[tex]\cos \phi = -1[/tex]
[tex]\phi = \pm\pi[/tex]
The position function for the object is:
[tex]x(t) = (13\,m)\cdot \cos \left[\frac{2\pi}{3}\cdot t \pm \pi\right][/tex], where t is measure in minutes.
