If F is a position dependent force given by F(x) = Ae-kx, where k is a positive constant, sketch the graphs showing F(t), v(t) and x(t) for v0 = 0 and x0 = 0. Show all salient points on your graphs and the behavior as x approaches infinity.
If F is a position dependent force given by F(x) = Ae-kx, where k is a...
A varying force is given by F=Ae^?kx, where x is the position; A and k are constants that have units of N and m^?1, respectively. What is the work done when x goes from 0.10 m to infinity? Express your answer in terms of the variables A, k, and appropriate constants. W=
The acceleration of a certain rocket is given by ax= bt, where b is a positive constant. (a) Find the position function x(t) if x = x0 and v0 at t = 0. (Use the following as necessary: x0, v0, b, and t.) x(t) = (b) Find the position and velocity at t = 7.9 s if x0 = 0, v0 = 0 and b = 3.3 m/s3. x(7.9 s) = m v(7.9 s) = m/s (c) Compute the average velocity of...
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of the region bounded by one arch of the graph f and the x -axis. b) Find the area of the triangle formed by the x -axis and the tangents to one arch nts to one arch of f at the points where the graph of f crosses the x -axis Let f(x) k sin(kx), where k is a positive constant (a) Find the area of...
Since no "m" term is given, does that mean there is no mass? (10%)5、GIVEN: bx+kx-F=8sin(ar) where b and k ROD: What value of o maximizes the amplitude of the steady state output, x,t) are positive constants and ω > 0 is a constant where x, (t) of course denotes the steady state part of x(t) IINI (10%)5、GIVEN: bx+kx-F=8sin(ar) where b and k ROD: What value of o maximizes the amplitude of the steady state output, x,t) are positive constants and...
Sketch the profile of the wave (x,t) = A sin(kx-t+), where the initial phase is given by each of the following: =0 , =/2 and 3. (20 points) Sketch the profile of the wave P(x,t) = A sin(kx-ot+E), where the initial phase is given by each of the following: E=0, E=1/2 and <=n.
A particle of mass m is moving in the potential . 1) Determine the force F(x) acting on the particle. Sketch the force and the potential in a single diagram, as functions of position, with . Find the physical dimension of constant A. 2) Find all equilibria of the particle on the interval . Determine whether these equilibria are stable or not. 3) If the initial position of x0 = a/2, find all possible values of initial velocity for which...
Consider the equation for a spring: d x(t) F = -kx = ma = mdt2 where This reduces to dax(t) +w2x(t) = 0 at² a) Verify that X(t) = Acos(wt + 1/2) is a solution by direct substitution. (2pts) b) Prove that Total Energy is conserved. (4pts) c) Prove that F is a restoring force to the equilibrium point x=0.(4pts)
E70.1(a) Construct the potential energy operator of a particle with potential energy V(x)={kx, where k is a constant.
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
1. The density function of b is given by kx(1 - x) f(x) = { for 0 < x 51, elsewhere. (a) Find k and graph the density function. (b) Find P(1/4 < ſ < 1/2). (c) Find P(-1/2 sã < 1/4). (d) Find the CDF and graph it. (e) Find E( ), E(52), and V(5). 1. The density function of ğ is given by |kx(1 – x) o for 0 < x 51, elsewhere. f(x (a) Find k and...