Here are several solutions curves in the phase plane. Which of these could be solutions of a harmonic oscillator
Q: A horizontal block spring oscillator of mass 10 kg on a frictionless table and spring constant…
A: Let m be the mass of the block, and k be the spring constant of the spring. Assume x to be the…
Q: How many nodes are there in the wavefunction of a harmonic oscillator with (i) v = 3; (ii) v = 4?
A: Part (i): The number of nodes in the wave function of a harmonic oscillator is, Here, v is the…
Q: The amplitude of a simple harmonic oscillator is doubled, How does it affect the total energy?
A: Relation between the total energy and amplitude is given as:
Q: 3. The motion of a mass-spring system with damping is governed by y"(t) +by' (1) + 16y(t) = 0; y(0)…
A:
Q: As shown above, the left end of a horizontal string is attached to an oscillator and the right end…
A: a) It is given that the velocity of the waves is less for the right half of the string than the…
Q: The original time period of the simple harmonic oscillator is T . if the spring constant k of the…
A: The time period of the simple harmonic oscillator and the spring constant k is related as
Q: A particle of mass m is located at a one-dimensional potential, a b U(x) x2 - Where the period of…
A:
Q: There are three particles of mass m connected to each other and to the walls by (light) springs as…
A: A) Newton's 2nd law for each particle is written as (in the order from left to right):…
Q: Two pendulums, both ending with mass m = 5 and with lengths l = 0.1 are coupled by a spring of…
A:
Q: Part A What is the magnitude of the momentum of a 31 g sparrow flying with a speed of 5.3 m/s?…
A:
Q: (5) A disc of radius R is rotating with constant angular velocity w about its center O. A pendulum…
A: A disc of radius R is rotating with constant angular velocity Now we have to find natural frequency…
Q: Find the general solution for a driven, undamped harmonic oscillator with driving force Fo sin(wot).…
A:
Q: Problem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute the time averages…
A:
Q: In Problem 28 nd the critical points and phase portrait of the given autonomous rst-order…
A: The objective of the question is to find the critical points and phase portrait of the given…
Here are several solutions curves in the phase plane. Which of these could be solutions of a harmonic oscillator
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite size ball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillati T = 2π The moment of inertia of the ball about an axis through the center of the ball is Here, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant of acceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball. Note, this pre-lab asks you to do some algebra, and may be a bit tricky. I mgh Iball = / mr² TA pendulum is a harmonic oscillator and suppose that once it is set into motion, it followssimple harmonic motion. We will assume that its equilibrium position is when it is hanging exactlyvertically at rest. When it is to the right of the equilibrium position it has positive displacement; to theleft of equilibrium position is negative displacement. For a particular pendulum, the following observations are made:• It is initially at its equilibrium position.• It is pushed to the right by a force to set it into motion at t = 0.• At its maximum displacement, it is 5 inches away from the equilibrium position.• It completes one cycle of motion in 0.5 seconds. a.) Determine a model for the displacement of the end of the pendulum d (in inches) as a functionof time t (in seconds). b.) At what times is the end of the pendulum furthest from the equilibrium position? There aremany times when this occurs due to the oscillation it experiences. List a few times and describe the patternwhat if a damped harmonic oscillator has a damping constant of beta= 2w, is this overdamping, critical damping, or underdamping? please explain why?
- Show the complete solutionA sinusoidal function has a minimum point at (2,4) it has an amplitude of 3. Use this to determine the equation of the midline and the value of the maximum. Explain with use of a sketchDetermine the theoretical equation for the dependence of Period of the Physical Pendulum to location of the pivot point for a solid bar of length L. This will be T(x) - Period as a function of pivot point position. Mathematically determine minima of the function T(x).
- The figure shows the top view of an object of mass m sitting on a horizontal frictionless surface, connected to two walls by two stretched rubber bands of length L. The tension in each rubber band is T when the object is stationary. Find an expression for the frequency of oscillations perpendicular to the rubber bands. Assume that the amplitude of oscilla- tions is sufficiently small such that the tension in the rubber bands is essentially unchanged as the object oscillates. Use small angle approximations to express your answer only in terms of the variables m, L and T. Rubber bandsA block of mass m = 2 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is initially at the equilibrium point at x = 0 m where the spring is at its natural length. Then theblock is set into a simple harmonic oscillation with an initial velocity 2.5 m/s at x = 0 cm towards right. Thehorizontal surface is frictionless. a) What is the period of block’s oscillation? b) Find the amplitude A of the oscillation, which is the farthest length spring is stretched to. c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motion graphx(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motion graph.Assume the clock starts from when the block is just released. d) Please find out the block’s acceleration when it is at position x = 5cm. e) On the motion graph you draw for part c), please mark with diamonds ♦ where the kinetic energy of theblock is totally transferred to the spring…Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite size ball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillati T = 2π The moment of inertia of the ball about an axis through the center of the ball is Here, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant of acceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball. Note, this pre-lab asks you to do some algebra, and may be a bit tricky. I mgh Iball = / mr² T
- By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions B-3 dimensionsA student wishes to measure the position of the oscillator. The best place to put the point of origin for the ruler is: A)At the positive Amplitude B)At the equilibrium position C) At the negative Amplitude D) At any convenient point the student chooses.Find the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.