Explanation Given information: The mass ( m ) of the bar is 3.6 kg. The length ( l ) of the bar is 750 mm. Assume the acceleration due to gravity ( g ) as 9.81 m/s 2 . Calculation: Show the position of displacement as in Figure (1). For position 1: Write the expression for mass moment of inertia rod ( I ): I = ( m l 2 3 ) Write the expression the velocity ( v m ) of bar: v m = l θ ˙ Write the expression for the kinetic energy ( T 1 ) : T 1 = 1 2 m v m 2 + 2 ( 1 2 I θ ˙ 2 ) Substitute ( m l 2 3 ) for I and l θ ˙ for v m . T 1 = 1 2 m ( l θ ˙ ) 2 + 2 ( 1 2 ( m l 2 3 ) θ ˙ 2 ) = 5 m l 2 6 θ ˙ 2 Write the expression for the potential energy ( V 1 ) : V 1 = 0 For position 2: Write the expression for the displacement ( h ) of bar AB : h = ( l 2 − l 2 cos θ ) = l 2 ( 1 − cos θ ) ( ∵ ( 1 − cos θ = 2 sin 2 θ 2 ) ) = l 2 2 sin 2 θ 2 For small oscillation 2 sin 2 θ 2 ≈ θ 2 2 . h = l 2 θ 2 2 = l 4 θ 2 Write the expression for the kinetic energy ( T 2 ) : T 2 = 0 Write the expression for the displacement ( h 1 ) of collar: h 1 = ( l − l cos θ ) = l ( 1 − cos θ ) ( ∵ ( 1 − cos θ = 2 sin 2 θ 2 ) ) = l ( 2 sin 2 θ 2 ) For small oscillation 2 sin 2 θ 2 ≈ θ 2 2

12th Edition

ISBN: 9781260265453

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 19.3, Problem 19.84P

To determine

The period (τn) of vibration of the system.

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Chapter 19.3, Problem 19.83P

Chapter 19.3, Problem 19.85P

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

Solution Summary: The author shows the position of displacement as in Figure (1).

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The period (τn) of vibration of the system.

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Chapter 19 Solutions