(a) Explanation Given information: The mass ( M ) of the cylinder is 6 kg. The mass ( m ) of the bar AB is 4 kg. The spring constant ( k ) is 5 kN/m . The amplitude ( x m ) is 12 mm. Calculation: Show the free body diagram of the cylinder and the bar AB as in Figure (1): Write the below equation by adding the horizontal force in the bar AB : m x ¨ = 2 k x − P (1) Write the below equation by adding the horizontal force in the cylinder: M x ¨ = P − F (2) Write the force ( F ) equation: F r = 1 2 M r 2 θ ¨ Substitute x ¨ r for θ ¨ . F r = 1 2 M r 2 x ¨ r F = 1 2 M x ¨ Substitute 1 2 M x ¨ for F in equation (2). M x ¨ = P − 1 2 M x ¨ Rewrite the above equation for P . M x ¨ + 1 2 M x ¨ = P P = 3 2 M x ¨ Substitute 3 2 M x ¨ for P in equation (1) (b) To determine The magnitude of the maximum velocity ( v m ) of bar AB .

12th Edition

ISBN: 9781265566296

Author: BEER

Publisher: MCG

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.2, Problem 19.39P

(a)

To determine

The period (τn) of vibration of the system.

(b)

To determine

The magnitude of the maximum velocity (vm) of bar AB.

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Chapter 19.2, Problem 19.38P

Chapter 19.2, Problem 19.40P

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The period ( τ n ) of vibration of the system.

Solution Summary: The author shows the free body diagram of the cylinder and the bar AB as in Figure 1.