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Express an equation for the simple harmonic motion that represents the graph displacement Y(m) versus time t(s) as shown in Figure below. [Ans: Y = 2 cos(1.57t) @Y = 2 sin (1.57t + Y(m) in A A t(s A harmonic oscillator oscillates with simple harmonic motion so that its position varies according to the expression * = 6.00 cos (3t+ where x is in centimetres and t is in seconds. Determine i) the position and acceleration of the particle at t = 0. ii) the amplitude and period of the motion [Ans: i)x=0.13 m; a=ms?; ii) A=0.06m; T=1 [Ans: T=1.29 s; L=0.41 m) According Figure : [ Ans:T=0.8 s; f = 1.25 Hz] (cm) kn 0.4 i. the period. ii. the frequency If the displacement in simple harmonic motion is given by y=A cos ot, show that the velocity of the particle is v = dy = w. A2 - y2 dx