Explanation Given: Mass of disk is 8 kg . Radius of disk is 200 mm . Static angle of rotation is 3 ° . Magnitude of static couple is 50 N-m . Maximum torsional couple is 60 N-m . Concept used: Write the expression for the amplitude of deflection in forced vibration. θ m = θ s t ( 1 − ( ω f 2 ω n 2 ) ) ...... (1) Here, θ m is the maximum amplitude of rotation angle, θ s t is the static rotation angle, ω f is the frequency of rotation and ω n is the natural frequency of system. Write the expression for torsional stiffness of spring. k = T θ ...... (2) Here, k is the torsional stiffness, T is the applied torque and θ is the angle of rotation by the applied torque. Write the expression for the moment of inertia of disk. I = 1 2 m r 2 ...... (3) Here, I is the moment of inertia of disk, m is the mass of disk and r is the radius of disk. Write the expression for natural frequency of system. ω n = k I ...... (4) Here, ω n is the natural frequency. Calculation: Substitute 50 N-m for T and 3 ° for θ in equation (2). k = 50 3 ° ( π 180 ° ) = 954.926 N-m/rad Substitute 8 kg for m and 200 mm for r in equation (3). I = 1 2 ( 8 ) ( 200 mm ( 1 m 1000 m ) ) 2 = 0.16 kg-m 2 Substitute 954

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ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 19.4, Problem 19.104P

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The range of value of ωf for which the amplitude of vibration is less than angle of rotation caused by static couple of magnitude Tm.

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Chapter 19.4, Problem 19.103P

Chapter 19.4, Problem 19.105P

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The range of value of ω f for which the amplitude of vibration is less than angle of rotation caused by static couple of magnitude T m .

Solution Summary: The author explains the expression for the amplitude of deflection in forced vibration and the moment of inertia of disk.

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The range of value of ωf for which the amplitude of vibration is less than angle of rotation caused by static couple of magnitude Tm.

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