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wp_hw_1_04

# wp_hw_1_04 - 1.138J/2.062J/18.376J WAVE PROPAGATION Fall...

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±± ±± 1.138J/2.062J/18.376J, WAVE PROPAGATION Fall, 2004 MIT C. C. Mei Homework set No. 1 1. A membrane is kept taut over an area S . The membrane has a constant density ρ per unit area and is under uniform tension in all directions. Derive the governing equa­ tion for the lateral displacment u ( x, y, t ) of the membrane vibrating under distributed loading of p ( x, t ) per unit area. 2. Consider the longitudinal vibration of a cylindrical rod with one end at x =0 ﬁxed and the other end at x = L attached to a mass M .B e f o r e t =0 th e rod i s compressed by the length ±L with ± ± 1. At t = 0 the compression is released. State the goverining equation and all boundary and initial conditions. 3. Condsider the torsional vibration of a cylindrical rod of circular cross section of radius a .Le t θ ( x, t ) = angular displacement of the cross section at x ,

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wp_hw_1_04 - 1.138J/2.062J/18.376J WAVE PROPAGATION Fall...

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