Show that for an underdamped harmonic oscillator (i.e., b < 2/sqrt(mk)), the position function can be expressed as x(t) = Be^(-(b/2m)t) cos(wt – phi) where w^2 = (4mk–b^2)/4m^2 and B is any constant.
Q: Question 10 If the function is given as U(x) = x4, is the equilibrium is stable at x=0? check your…
A:
Q: (a) An oscillating object of mass m, obeys the governing equation my" + cy' + ky = F(t) subject to…
A:
Q: A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for…
A: The required solution is following.
Q: which the Lagrangian is I = mc² (1-√√1-B²)-kx² where ß = == a) Obtain the Lagrange equation of…
A: Required to find the equation of motion.
Q: 3. (1) To find the deflection of the simply supported beam by using Fourier Sine series. q is the…
A: EI =d4ydx4+Nd2ydx2-qx =0
Q: Find the expected ualue of the Harmonic oscillator function Un lx) =Nexp ( *z) Hn Lx)
A: it is required to find the expected value of the given harmonic oscillator function. Here the given…
Q: cillator, show the raising
A: The proof of commutation relations as,
Q: (a) Show that the transformation Q = p + iaq, P = (p − iaq) / (2ia) is canonical and find a…
A:
Q: you know that the escilator drops to 1/5 of its initial values after using it from the full…
A: It is known that the waning frequency is calculated as, ωd=ωn1-ζ2, where ωn is the natural…
Q: There is a pendulum in an elevator going down with constant velocity v. Assuming the mass of the…
A:
Q: 12.1 Consider the nonlinear first-order equation x = 2√x - 1. (a) By separating solution x₁(1). (b)…
A:
Q: In the physical system of unit particles in a one-dimensional harmonic oscillator described at time…
A:
Q: Consider the case of a one-dimensional harmonic ocillator. Suppose x is the displacement coordinate.…
A: Note: Thank you for the information, But as in the question, it is not mentioned that what action to…
Q: Example 1: A particle is executing simple harmonic motion of period Tabout a centre O andit passes…
A: Let the time measured from A, then X=acos(muot)
Q: What is ?, , ² and ² for µ1 of a harmonic oscillator? Show complete derivation.
A: As per our policy, first three subparts will be answered. Given: For harmonic oscillator,…
Q: Given an infinite well of length 0 to L, and an initial wavefunction which is a tent shaped…
A:
Q: A 5-kg mass is attached to a spring with stiffness k= 20 N/m. The mass is displaced m to the left of…
A: A massattached to a spring constantInitially i.e. at t=0sy(0)=0.25mand
Q: The energy E of a system of three independent harmonic oscillators is given by 1 1 E = (nx + ½ )ħw +…
A:
Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² +…
A: Let the given particle is the electron. Then the transition probability (W) be given as, Where, ω…
Q: Consider the one-dimensional linear chain in which the force constants neighbor atoms are…
A: The dispersion relation for the frequency is ω2=1MC1+C2±C12+C22+2C1C2coska (a) The value of ω2 for…
Q: 3. A simple harmonic oscillator makes 25 complete vibrations after 5.0 seconds. Determine its (a)…
A:
Q: Assume that the given function is periodically extended outside the original range. Find the…
A: The Fourier series of a periodic function f(x) with period 2L can be written as the sum of an…
Q: Using the matrix expression for A and of the harmonic oscillator, find the matrix representations of…
A:
Q: Consider a particle subject to a linear restoring force F=-kx, where k is a constant and x is the…
A:
Q: Prob.1 (1) State the required conditions of simple harmonic motion (SHH).
A: We need to find the necessary condition for simple harmonic motion.
Q: Show that the minimum energy of a simple harmonic oscillator is hω/2. What is the minimum energy in…
A: The mean value of x2av is the mean square devation ∆x2By substituting the mean square deviation…
Q: State the required conditions of simple harmonic motion (SHH). Consider the torsional pendulum with…
A: (i) There are two main conditions for a motion to be classified as SHM: The magnitude of the…
Q: f(x, y) = (cos(x) + cos(yV3/2 – a/2) + cos(yv3/2+x/2))² Plot the contours of this function for -3…
A: A contour plot is a graphical method to visualize the 3-D surface by plotting constant Z slices…
Q: matrix element of p² be
A:
Q: How to solve %diff in t just for on secti
A: Solution: 1. The mathematical expression for the time period is given by, T=2πMTK From the above…
Q: The Longrongion of 1D harmonic is, ()- write Euler-Congrange equation of system? ().write…
A:
Q: Write the vector function for the harmonic oscillator using the generator function, then find the…
A: The generator function for the harmonic oscillator is given by: G(u) = (mω^2/2u^2 - iu/2)^(-1/2)…
Q: mass of 12 slugs is hanging at rest on a frictionless spring whose constant is k = 1/3 . Beginning…
A: Given: The spring constant k=1/3. The external force is Ft=20 cosωt. To find: (a) The…
Q: Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency…
A:
Q: A laminar boundary layer profile may be assumed to be approximately of the form u/U₁ = f(n) = f(y/6)…
A: Step 1: Understanding the Velocity ProfileThe velocity profile is given in two segments:where…
Q: Exercise b. A 24 lb weight stretches a spring 12 inches. If the weight is pulled 10 inches below the…
A:
Q: Lindstedt
A:
Q: A mass of 55 grams stretches a spring by 8 cm. (Note that this means the forces balance, and thus mg…
A: m = 55 gram g = 981 m/s2 x= 8cm Initial velocity v= 23 cm/s = 0.23 m/s We can see that the particle…
Q: A double pendulum consists of two equal masses 'm' suspended by two strings of length L. What is the…
A: Solution: The free-body diagram is
Q: The Longrongion of 1D harmonic oscilator 1 = ² ² ²x² ах 2 m. 2 () write Euler-Longronge equation of…
A: Lagrangian is difference of kinetic and potential energy.…
Q: By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions B-3…
A: For a Harmonic oscillator, the Kinetic energy T and Potential Energy V are given by, Considering…
Q: Table 2 Trial 1 2 3 4 MV Jov ng equations (1) through (3), to eliminate v, yields w the pendulum to…
A: The given data table is: Trial Angle (θ) ∆h 1 39 6.68 2 39.5 6.85 3 39.5 6.85 4 39 6.68…
Show that for an underdamped harmonic oscillator (i.e., b < 2/sqrt(mk)), the position function can be expressed as x(t) = Be^(-(b/2m)t) cos(wt – phi) where w^2 = (4mk–b^2)/4m^2 and B is any constant.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps