Python 2: vào năm 2000, Guido và nhóm phát triển Python dời đến và thành lập BeOpen PythonLabs team. Phiên bản Python được phát hành tại đây. Sau khi phát hành Python , Guido và các thành viên PythonLabs gia nhập Digital Creations. | 209 Romberg Integration The figure shows an elastic half-space that carries uniform loading of intensity q over a circular area of radius a. The vertical displacement of the surface at point P can be shown to be 1 n 2 cos2 0 w r w0 I d0 r a 0 ự r a 2 - sin2 0 where w0 is the displacement at r a. Use numerical integration to determine w w0 at r 2a. 13. The mass m is attached to a spring of free length b and stiffness k. The coefficient of friction between the mass and the horizontal rod is X. The acceleration of the mass can be shown to be you may wish to prove this x f x where fc b X f x Xg m w x V 4bP x2 If the mass is released from rest at x b its speed at x 0 is given by v0 2 f x dx 0 Compute v0 by numerical integration using the data m kg b m X k 80 N m and g m s2. 14. Debye s formula for the heat capacity CV of a solid is CV 9Nkg u where f 1 U ỵApx g u 3 e Õ2dx The terms in this equation are N number of particles in the solid k Boltzmann constant u T D T absolute temperature D Debye temperature Compute g u from u 0 to in intervals of and plot the results. 210 Numerical Integration 15. A power spike in an electric circuit results in the current i t i0e t t0 sin 2t Z0 across a resistor. The energy E dissipated by the resistor is E R i t 2 dt 0 Find E using the data i0 100 A R and t0 s. 16. An alternating electric current is described by i t io f sin p sin t0 t0 where i0 1 A t0 s and p . Compute the root-mean-square current defined as . 1 Íf0 irms t dt t0 0 17. a Derive the composite trapezoidal rule for unevenly spaced data. b Consider the stress-strain diagram obtained from a uniaxial tension test. The area under the diagram is Ar i s a ds 0 where sr is the strain at rupture. This area represents the work that must be performed on a unit volume of the test specimen in order to cause rupture it is called the modulus of toughness. Use the result of Part a to estimate the 211 Gaussian Integration modulus of .
