Question

The figure below shows a crude model of an insect wing. d2 di m F The mass, m, represents the entire mass of the wing, which pivots about the fulcrum, F. The spring represents the surrounding connective tissue. Motion of the wing corresponds to vibration of the spring. Suppose the mass of the wing is 0.285g and the effective spring constant of the tissue is 4.56E-4 N/m. Distance d, = 3.17 mm and distance d2 = 1.47 cm. If the mass m moves up and down a distance of 2.04 mm from its position of equilibrium, what is the maximum speed of the outer tip of the wing?

Answer 1

Since the inner tip of the wing is attached to the end of the spring, it always moves with the same speed as the end of the vibrating spring. The maximum velocity of oscillating system is given by, (2.04mm) m lcm 4.5x104N/m **?10mm ) V 0.285x10-kg = 0.256cm/s The maximum speed of the inner tip is 0.256cm/s. The expression for the angular speed of the innertip is, l'inner The expression for the angular speed of the innertip is, V Outer outer = outer router As the angular velocities of the tips are equal, equate the expressions for angular speed, Vinner - Vouter (1) Pinner router Solve equation (1) the expression for the maximum speed of the outer tip of the wing. "outer outer Vouter, max Vinner, mas Tinner ) 10 mm 1.47cmx3 Icm 3.17mm (0.256cm/s) VA outer ,max 1 1.19 cm/s