Explanation Given: Mass of the sphere is 2 kg , mass of the rod is 1.5 kg , length of the rod is 2 kg and spring constant is 200 N/m . Concept used: Conservation of energy for a vibrating system is given as follows: ∑ K E = ∑ P E ..... (1) Here, maximum kinetic energy is K E , maximum potential energy is P E . Calculation: Mass moment of inertia can be expressed as follows: I = m l 2 Substitute 1 2 I ω 2 for ∑ K E and 1 2 k ( a sin θ ) 2 − m g l ( 1 − cos θ ) for ∑ P E in equation (1). 1 2 I o ω 2 = 1 2 k ( a sin θ m ) 2 − m g l ( 1 − cos θ m ) 1 2 m l 2 θ ˙ m 2 = 1 2 k ( a θ m ) 2 − m g l ( θ m 2 2 ) < To determine (b) The smallest value of ‘ a’ for oscillations occur.

12th Edition

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 19.3, Problem 19.89P

To determine

(a)

The frequency of oscillations.

To determine

(b)

The smallest value of ‘ a’ for oscillations occur.

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Chapter 19.3, Problem 19.88P

Chapter 19.3, Problem 19.90P

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(a) The frequency of oscillations.

Solution Summary: The author explains the frequency of oscillations in a vibrating system.