Solve the harmonic oscillator motion for initial conditions x(0) = 0, V(0) = V0 in the case of (a) underdamped (b) overdamped
Try the solution of the form
(a) Roots are complex conjugates,
where
The general solution is
I can always adjust A' and B' such that exponential of imaginary quantities are removed using Euler's relation. So the general solution is
For arbitrary constants A and B, to be determined by initial conditions which are
which imply
(b)
Roots are real,
where
The general solution is
As before adjust A' and B' so that the solutions look more stylish! Use hyperbolic functions this time
For arbitrary constants A and B, to be determined by initial conditions which are
which imply
Solve the harmonic oscillator motion for initial conditions x(0) = 0, V(0) = V0 in the...
2. Solve for the motion of a driven-damped harmonic oscillator whose forcing function F(t) is given by F(t) = 0, < 0 HU t 12 0 <t<T PO) – 4(), 0<t<7 F(t) = A, t>t. m т.
sin 0, cos 0 Name the quadrant in which the angle lies We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup norm. Let x and f X. Show that the non linear integral equation u(x) = (sin u(y) dy + f(x) ) has a solution u X. (the integral is from a to b). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Calculate the work done by the vector field F(x,y)=4xy, 2x2 along a smooth, simple curve from point (3, −1) to point (4, 2) We were unable to transcribe this imageWe were unable to transcribe this image
Prove, or give a counter example to disprove the following statements. a) b) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let f(x)= if , if if a) What is the fomain of f(x)? Write in interval notation. b) Determine the y-intercept of the function, if any. Make sure to justify your answer. c) Determine the x-intercepts of the function, if any. Justify your answer. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Please help solve this, using the equation to get through the problem. Additional information: where the initial position , the initial speed The above differential equation can also be written as: If , there is light damping where the solution has the form ( where r and w are two positive constants) or If there is heavy damping where, where and are two positive constants If there is critical damping where, where r is a positive constant d'y dy ma...
COMPLEX ANALYSIS: Solve the integral where and . Please use JORDAN'S LEMMA and show all of your work. Thank you! We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A consumer with convex, monotonic preferences consumes non-negative amount of and . This consumer faces the budget constraint and has the utility function where a) Derive the indirect utility function. b) Derive the expenditure function. c) Explain briefly according to your understanding the link between direct, indirect and expediture function. We were unable to transcribe this imageWe were unable to transcribe this image2121 +22p2 <y u(r1, 72) = riz-a 0 <α<
Suppose that is a bounded function with following Lower and Upper Integrals: and a) Prove that for every , there exists a partition of such that the difference between the upper and lower sums satisfies . b) Furthermore, does there have to be a subdivision such that . Either prove it or find a counterexample and show to the contrary. We were unable to transcribe this imageWe were unable to transcribe this image2014 We were unable to transcribe this...