To determine The changes in the harmonic oscillation if the mass is doubled and if a spring of twice the modulus is taken. Explanation It is known that, the frequency of a harmonic oscillation is f = ω 0 2 π Hertz , where ω 0 = k m and m represents the mass and k represents the spring constant. Case (i) Consider the mass of the spring as double of the mass. Compute the frequency of the spring as follows. Substitute m = 2 m in ω 1 = k m . ω 1 = k 2 m = 1 2 ⋅ k m = 1 2 ⋅ k m = 1 2 ω 0 [ ∵ ω 0 = k m ] That implies, f 1 = ω 1 2 π = 1 2 f Thus, if the mass is doubled, then the frequency of harmonic oscillation is decreases by 2 times than the original frequency _

Custom Kreyszig: Advanced Engineering Mathematics

10th Edition

ISBN: 9781119166856

Author: Kreyszig

Publisher: JOHN WILEY+SONS INC.CUSTOM

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Chapter 2.4, Problem 3P

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The changes in the harmonic oscillation if the mass is doubled and if a spring of twice the modulus is taken.

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Chapter 2.4, Problem 2P

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