Section B Formula sheet for questions 4-6. mx + cx + kx = F sin cot Χ _ 2πζω, 275 8=In = = X₂ @d 1-5² 2π = 0,₁ √1-5² @d *+250x+x=0 F X = [(k_o²m)² + (oxc)² ]/² CxXxX (k − w²m) tano = Where m= mass (kg) c= damping coefficient (Ns/m) k = spring stiffness (N/m) F = harmonic force (N) w = harmonic frequency (rad/s) 8 = logarithmic decrement Wn ural frequency (rad/s) @d damping frequency (rad/s) =damping ratio Td = damping period (s) *1/x₂= ratio of successive peaks X = amplitude of vibration Ø=phase angle (0) =nat- = Question 4 The instantaneous position of a four-bar linkage mechanism is shown in figure 1. The input link, AB, rotates anticlockwise at N = 800 rev/min. AB = 2.5m, AD = 2m, CD = 2m, BAD = 120⁰ and CDA =100°. a. Draw the velocity diagram describing this mechanism's motion. Showing magnitudes and directions. [15 marks] b. Determine the angular velocity of the output link, CD about D. [5 marks] B @2 2m Figure 1
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