Derive the relationship between phase and group velocity . elaborate the cases where both are equal and also when both are different and also find the value of displacement when K.E=P.E?
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Derive the relationship between phase and group velocity . elaborate the cases where both are equal and also when both are different and also find the value of displacement when K.E=P.E?
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- function of r. Consider a small displacement r= Ro+r' and use the binomial theorem: (1+x)" = 1+ nx + 2! п(п — 1) n(n — 1)(n — 2) з + -x' + 3! to show that the force does approximate a Hooke's law force. 71. Consider the der Waals potential van 12 U(r) = U. used model the to potential energy function of two molecules, where the minimum potential is at r = Ro. Find the force as aAn oscillating water sprinkler is operated at point A on an incline that forms an angle ß with the horizontal. The sprinkler discharges water with an initial velocity vo at an angle 0 with the vertical which varies from -6, to +6. Knowing that vo-37 f/s, 6,-50°, B=15°, determine the horizontal distance between the sprinkler and points B and C which define the watered area. +e. B A Re R.Why is Logger Pro set up to report the time between every other blocking of the Photogate? Why not the time between every block? Using either Graphical Analysis or graph paper, plot a graph of pendulum period vs. amplitude in degrees. Scale each axis from the origin (0,0). Does the period depend on amplitude? Explain. Using either Graphical Analysis or graph paper, plot a graph of pendulum period T vs. lengthl. Scale each axis from the origin (0,0). Does the period appear to depend on length? Using either Graphical Analysis or graph paper, plot the pendulum period vs. mass. Scale each axis from the origin (0,0). Does the period appear to depend on mass? Do you have enough data to answer conclusively? To examine more carefully how the period T depends on the pendulum length l, create the following two additional graphs of the same data: T 2 vs. l and T vs. l2 . Of the three period-length graphs, which is closest to a direct proportion; that is, which plot is most nearly a straight line…
- Window 15 660 118% specified (x, y) for a point particle in 3-space, one is still free to choose z independently of the assigned values of x and y. PROBLEMS 1.1 For each of the following systems, specify the number of degrees of freedom and a set of good coordinates. (a) A bead constrained to move on a closed circular hoop that is fixed in space. (b) A bead constrained to move on a helix of constant pitch and constant radius. (c) A particle on a right circular cylinder. (d) A pair of scissors on a plane. (e) A rigid rod in 3-space. (f) A rigid cross in 3-space. (g) A linear spring in 3-space. (h) Any rigid body with one point fixed. (i) A hydrogen atom. (j) A lithium atom. (k) A compound pendulum (two pendulums attached end to end). 1.2 Show that a particle constrained to move on a curve of any shape has one degree of freedom. Answer Aurye ie none dimancionalleous an DOLLFor Parts I and II, use the pendulum equation and solve to predict the length needed for a pendulum with a period of 1 s and 2 s respectively. Use a piece of string (or thread, dental floss, shoe lace, etc.) and a steel nut (or washer or something small but with enough mass to weigh down the string) to build each pendulum. Time each pendulum for 30 periods and then find the average time for one period. Remember, a period is the time to complete one cycle of motion, out and back. Tape each pendulum up in perhaps a doorway where it is stationary and has room to swing. Be precise with your measuring and timing. Show your work. Part I Given: T = 1.00 s l =? Part II Given: T = 2.00 s l =?A small piece of rounded stone perforated for threading is sliding on a wire which is hanging freely in the shape of a cosh function. Assume the stone moves with no friction. For very small displacements in x, what is the frequency of oscillation? You may use for the height of the wire and thus the height of the stone as a function of x the Taylor series expansion of cosh. G(x) =1 + x2/2 + x4/24 + ...