Visualizing simple harmonic motion 0.08.0 points {graded} To answer the toilowing questions, refer to the figure shown here. Note that the initial position is :c = 2.25 m. D 0.4 0.8 1 2 1.6 2 f (S) (a) Suppose that the figure depicts the displacement of a mass in a horizontal mess-spring system as a function oftime. Draw the mass~spring system at time: : D 5. Label the positions as : A, z : A in addition to a: (t = 0), where A represents the amplitude. Draw an arrow to indicate which direction the mass is travelling. [bl 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 = U s. [c] If the simple harmonic motion of the mass is described by a wave y {t} 2 Aces (wt + (9)]. determine the amplitude A, angular frequency no, and phase constant d), and write the function in terms of these values [give the angular frequency and phase constant to three signicant digits}. [Hint: When determining the phase constantr you may we nt to refer to your diagram in part tbi]. {I} The amplitude A is the maximum positive displacement. A 2 m [ii] The angular frequency to is related to the period byw anT, where T is the period at one full cycle. w : [iii] The initial phase tbs describes the particle's initial angular position. Express on as an angle between 0 and 2'7- 9'5'0 = As the ware, is travelling from + 3 to - 3 , S6 therefore the amplitude of the wave is A = 3 m ( is ) The angular frequency w is related to the period , . w = 21 J T is the time period of full cycle - 2 , here . So , Therefore , w = (21 -7w = 1 S (in ) The initial phase is p . so , minimum angle of the phase is oo and maximumn angle of the phase is 21 . Therefore , P. = 0