Final answer:
The position of the object at t = 0 is 0.70 m and at t = 0.20 s is approximately 0.695 m. The amplitude of the motion is 0.70 m. The frequency of the motion is approximately 2π/9 Hz.
Step-by-step explanation:
In the given equation x = (0.70 m) cos(t/9), we can find the position of the object by substituting the given values of t into the equation. At t = 0, the position of the object is x = (0.70 m) cos(0/9) = 0.70 m. At t = 0.20 s, the position of the object is x = (0.70 m) cos(0.20/9) ≈ 0.695 m.
The amplitude of the motion is the maximum displacement from the equilibrium position. In this case, the amplitude is 0.70 m.
The frequency of the motion is the number of cycles completed per unit of time. In this case, the frequency can be calculated using the formula f = 1/T, where T is the period. The period of the motion is the time it takes for one complete cycle, and it can be calculated using the formula T = 2π/ω, where ω is the angular frequency. In this case, the angular frequency is 2π/9 rad/s, so the period is T ≈ 9/2π s. Therefore, the frequency is f ≈ 2π/9 Hz.