1000 Solved Problems in Modern Physics by Ahmad A. Kamal

By Ahmad A. Kamal

This e-book primarily caters to the desires of undergraduates and graduates physics scholars within the zone of contemporary physics, specifically particle and nuclear physics. Lecturers/tutors may possibly use it as a source e-book. The contents of the ebook are according to the syllabi at present utilized in the undergraduate classes in united states, U.K., and different international locations. The publication is split into 10 chapters, every one bankruptcy starting with a quick yet sufficient precis and beneficial formulation, tables and line diagrams by way of quite a few standard difficulties helpful for assignments and checks. unique suggestions are supplied on the finish of every chapter.

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Assume that m 1 = m 2 = m and the stiffness constant is k for both the oscillators. (a) Form the differential equations for both the oscillators and solve the coupled equations and obtain the frequencies of oscillations. (b) Discuss the modes of oscillation and sketch the modes. Fig. 62 A cylinder of mass m is allowed to roll on a spring attached to it so that it encounters simple harmonic motion about the equilibrium position. Use the energy conservation to form the differential equation. Solve the equation and find the time period of oscillation.

48 Find the area of the surface of revolution generated by revolving the hypocycloid x 2/3 + y 2/3 = a 2/3 about the x-axis. 50 Calculate the area of the region enclosed between the curve y = 1/x, the curve y = −1/x, and the lines x = 1 and x = 2. 53 (a) Calculate the area bounded by the curves y = x 2 + 2 and y = x − 1 and the lines x = −1 to the left and x = 2 to the right. (b) Find the volume of the solid of revolution obtained by rotating the area enclosed by the lines x = 0, y = 0, x = 2 and 2x + y = 5 through 2π radians about the y-axis.

Y 3 1 3 x+ ⎟ ⎟ ⎜ ⎜ cos 30◦ sin 30◦ x 2 √2 ⎟ x 2 √2 ⎟ DX = ⎜ =⎜ ⎝ 1 3 ⎠ y = − sin 30◦ cos 30◦ ⎝ x y 3 ⎠ − − + y 2 2 2 2 The matrix D is a rotation matrix which rotates the vector through 30◦ about the z-axis,. 10d. Fig. 30, the characteristic roots are found to be λ = 2, 2, 8. With λ = 2, we find the invariant vectors. ⎛ ⎞⎛ ⎞ 6 − 2 −2 2 x1 ⎝ −2 3 − 2 −1 ⎠ ⎝ x 2 ⎠ = 0 x3 2 −1 3 − 2 The two vectors are X 1 = (1, 1, −1) and X 2 = (0, 1, 1) . The third vector can be obtained in a similar fashion.

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