A simple harmonic oscillator has a total energy given by the function E = 100 J/m2 ? x 2 + 100 J · s 2 /m2 ? v 2 x What is the angular frequency of this oscillation
A simple harmonic oscillator has a total energy given by the function E = 100 J/m2...
[20 points] A particle in the simple harmonic oscillator potential with angular frequency a is initially in the ground state: c,y, (x) =Yo(x Att = 0 , the angular frequency of the oscillator suddenly doubles: a} → a½-2.4 The initial wave function can be written in terms of the modified potential (denoted with a tilde:~: Recall that the general form of the first few stationary states for the harmonic oscillator are given on page 56 of your text. a. What...
1. The solution for a SHO (simple harmonic oscillator) is given as: x(t) = 0.1 sin(3t − π/6) meters. Include appropriate units in your answers. (a) What is the amplitude of oscillation? (b) What is the initial position of the oscillator? (c) What is the maximum velocity of the oscillator and at what value of x does it occur? (d) What is the maximum acceleration of the oscillator and where does it occur? (e) What are the period and frequency...
1. Consider a one-dimensional simple harmonic oscillator. We know that the total energy (E) has values: Here the angular frequency (o) corresponds to the freshman physics value of [spring constant/massja and (n) can be 0, 1,2, any non-negative integer. We know that the total energy is a measurable, observable quantity. The total energy includes the kinetic energy and the potential energy. Please explain whether or not the kinetic energy and the potential energy can both be measured at the same...
Name: A simple harmonic oscillator has a period of oscillation of 0.33 s. What is the frequency of the 1. oscillator? a. 0.053 Hz b. 0.33 Hz c. 2.1 Hz d. 3.0 Hz e. 19 Hz
For a simple harmonic oscillator determine a total energy b the kinetic energy and potential energy at half amplitud x=A/2
A) The velocity of a simple harmonic oscillator is given by v = -7.35sin(26.8t) (mks units) What is its angular frequency? B) What is the amplitude of the motion in Problem 1 in meters to two decimal places? C) To the nearest hundredth of a meter where is the mass in Problem 1 at the time t = 44.03 seconds? D) If the mass in Problem C is 0.75 kg, what is the spring's potential energy to the nearest tenth...
Estimate the ground-state energy of a one-dimensional simple harmonic oscillator using (50) = e-a-l as a trial function with a to be varied. For a simple harmonic oscillator we have H + jmwºr? Recall that, for the variational method, the trial function (HO) gives an expectation value of H such that (016) > Eo, where Eo is the ground state energy. You may use: n! dH() ||= TH(c) – z[1 – H(r)], 8(2), dx S." arcade an+1 where (x) and...
The position of an OAS (Simple Harmonic Oscillator) as a function of time is given by x = 3.8m cos (1.25t + 0.52) where t is in seconds and x is in meters Find a) Period (s) b) Acceleration (m / s^2) at t = 2.0s
h2 4. In a region of the x-axis, a particle has a wave function given by y(x) = Ae-*4722° and energy where L is some length. (a) Find the potential energy as a function of x, and sketch V (x) versus x. (b) What is the classical potential (or corresponding force function) that has this dependence? (c) Find the kinetic energy as a function of x. (d) Show that x = L is the classical turning point (i.e. the place...
For a particle described as a harmonic oscillator, the total energy w given by E,- (n + hy and the potential energy is piven by VG) kw The classical turning points, to are the values of x where the total energy is equal to the potential energy. The ground state wave function of a harc oscillator is . The cost is defined by a = k/?. If we define the variable y as y = x, which of the following...