Is an oscillator whose restoring force is F = -kx2 a simple harmonic oscillator?
F = -kx , is the restoring force for simple harmonic oscillator.
So the given oscillator is not a simple harmonic oscillator.
Is an oscillator whose restoring force is F = -kx2 a simple harmonic oscillator?
Consider a one-dimensional simple harmonic oscillator under the influence of a restoring force -kx. Find its average displacemtnt, average speed, average potential energy within a quater of its time period.
3. Consider the simple harmonic oscillator. sub) Simple harmonic oscillator, subject to an external force f.my' + ky = f. whereby m, k > 0, with initial conditions y(0) > 0. with initial conditions (0) = 0 and y(0) = 0. Find the solution given that (i) f(t) = 2: (ii) f(t) = e'; (iii) f(t) = sint, k m ; (iv) f(t) = sint, k=m.
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
simple harmonic motion If you apply Newton's Second Law to a linear restoring force, you obtain d x dt Determine if the following function is a solution to the above differential equation. x(t)- Ae wherei--1 ieot
The expression for the acceleration of a certain simple harmonic oscillator is given by a = – (20 m/s2) cos (2.5t). a. Calculate the amplitude of the simple harmonic motion. b. Write an expression for the velocity of the same simple harmonic oscillator c. Write and expression for the displacement of the same simple harmonic oscillator
Question no 6.1, statistical physics by Reif Volume 5 Problems 6.1 Phase space of a classical harmonic oscillator The energy of a one-dimensional harmonic oscillator, whose position coordinate is x and whose momentum is p, is given by where the first term on the right is its kinetic and the second term its potential energy. Here m denotes the mass of the osellating particle and a the spring constant of the restoring force acting on the particle. Consider an ensemble...
1. The amplitude of a simple harmonic oscillator is doubled. Which of the following remain the same? O O O O a The maximum velocity b.The maximum acceleration. c. The frequency. d. All of them remain the same. O eNone of them remain the same 2. Suppose a special spring is made that has an unusual force law. The force law of ths spng is F--kx3. The motion of a mass attached to this spring will be O a simple...
As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba- bility to find the new oscillator in an excited state. As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba-...
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.
A simple harmonic oscillator at the position x=0 generates a wave on a string. The oscillator moves up and down at a frequency of 40.0 Hz and with an amplitude of 3.00 cm. At time t = 0, the oscillator is passing through the origin and moving down. The string has a linear mass density of 50.0 g/m and is stretched with a tension of 5.00 N. A simple harmonic oscillator at the position x = 0 generates a wave...