Question

\sigma = \gamma_0 (G' \sin \omega t + G'' \cos \omega t) Show that the component of the stress in phase with the strain produces a net-zero absorption of energy by the sample in one cycle of the test.

          \sigma = \gamma_0 (G' \sin \omega t + G'' \cos \omega t)
Show that the component of the stress in phase with the strain produces a net-zero absorption of energy by the sample in one cycle of the test.

σ= γ0 (G' sinωt + G” cosωt)
Show that the component of the stress in phase with the strain produces a net-zero absorption of energy by the sample in one cycle of the test.

Added by Laura K.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Surjit Tewari

Step 1

This means that we are only interested in the term involving sin wt. So, we can rewrite the equation as: 0 = YoGsin wt Since the equation equals zero, this means that the stress component in phase with the strain is always zero. In other words, there is no net Show more…

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0 = Yo(G'sin wt + G"cos wt) Show that the component of the stress in phase with the strain produces a net-zero absorption of energy by the sample in one cycle of the test.