Visualizing simple harmonic motion 0.0/3.0 points (graded) To answer the following questions, refer to the figure shown here. Note that the initial position is x = -2.25 m. x (m) 3 1.5 M -1.5 -3 0 0.4 0.8 1.2 1.6 2 t(s) (a) Suppose that the figure depicts the displacement of a mass in a horizontal mass-spring system as a function of time. Draw the mass-spring system at time t = 0 s. Label the positions x = A, x = -A in addition to x (t = 0), where A represents the amplitude. Draw an arrow to indicate which direction the mass is travelling. (b) Simple harmonic motion can also be represented as the periodic motion of a point moving on the unit circle. Draw a unit circle, and indicate the point on the unit circle representing the system at time t = 0 s. (c) If the simple harmonic motion of the mass is described by a wave y (t) = Acos (wt), determine the amplitude A, angular frequency w, and phase constant o, and write the function in terms of these values (give the angular frequency and phase constant to three significant digits). [Hint: When determining the phase constant, you may want to refer to your diagram in part (b)). (i) The amplitude A is the maximum positive displacement. A = m (ii) The angular frequency w is related to the period by w = 2T/T, where T is the period of one full cycle. W = (iii) The initial phase do describes the particle's initial angular position. Express do as an angle between 0 and = 2. |