Question

Please answer problem 3 a, b, c, d and problem 4

Problem 3: solve Ginsberg problem 2.3 using a sine and/or cosine representation Use the properties in this trace to determine (a) The initial values of x and (b) The value of t at which the minimum value ofx first occurs. (c) The maximum positive value of and the ear- liest value of t at which this maximum occurs. (d) The maximum positive value of and the ear- liest value of t at which this maximum occurs. 1 ms 3 ms 20 mm EXERCISE 2.3 Problem 4: resolve Ginsberg problem 2.3 using a complex exponential representation

Answer 1

Given: T/2 = 3 ms t rightarrow x_max = 20 mm x = x_max sin (wt + phi) phi is the phase difference w = 2 pi v: v = 1/T Rightarrow w = 2 pi/6 ms x = 20 sin (2 pi/6 times t + phi) condition t = 1 ms , x = 0 0 = 20 sin (2 pi/6 + phi) Rightarrow pi/3 + phi = pi phi = 2 pi/3 Therefore x = 20 sin (2 pi/6 times t + 2 pi/3) where t rightarrow milli-sec x rightarrow mm a) x = 20 times 2 pi/6 times cos (2 pi/6 times t + 2 pi/3) at t = 0 x = 20 times 2 pi/6 times -0.5 = 10.471 mm/ms = 10.471 m/s at t = 0 x = 20 times 0.866 = 17.32 mm \r\n b) This can be calculated directly from the graph t = 1 + 1 .5 = 2.5 ms c) max x = 20 times 2 pi/6 = 20.94 m/s