Explanation Given information: Period of vibration τ 1 = 0.58 s Period of vibration τ 2 = 1.8 s Density of oil ρ = 900 Κ g / m 3 Diameter of the barrel D = 572 m m The mass of the barrel is calculated by using the formula given below: ω 1 ω 2 = k m e m p . b a r r e k m o i l + m e m p . b a r r e For this first we have to calculate the natural frequency in both the cases that is; when the barrel is empty and when is filled with oil. Case I: when barrel is empty. Period of vibration τ 1 = 2 π ω 1 0.58 = 2 π ω 1 ω 1 = 2 × 3.14 0.58 ω 1 = 10.83 r a d / s Thus, ω 1 = k m e m p . b a r r e ____________ (1) Case II: when barrel is filled with oil. The mass of oil m o i l = 55 × 1 264.172 × 900 m o i l = 187.378 Κ g Now, period of vibration τ 2 = 2 π ω 2 1.8 = 2 × 3.14 ω 2 ω 2 = 2 × 3.14 1.8 ω 2 = 3.49 r a d / s Thus, ω 2 = k m o i l + m e m p To determine (b) The density of the salt water.

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ISBN: 9781260265521

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 19.1, Problem 19.26P

To determine

(a)

The mass of empty barrel.

To determine

(b)

The density of the salt water.

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Chapter 19.1, Problem 19.25P

Chapter 19.1, Problem 19.27P

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(a) The mass of empty barrel.

Solution Summary: The author explains that the mass of the barrel is calculated by using the formula given below.