Question

In: Physics

1) What is ? for a harmonic oscillator (in terms of the period)?

 

1) What is ? for a harmonic oscillator (in terms of the period)?

2) What is ? for a spring?

A) If you increase the amplitude, what happens to the period?

B) If you increase the mass, what happens to the period?

C) If you increase the spring constant, what happens to the period?

3) What is ? for a simple pendulum?

A) If you increase the amplitude, what happens to the period?

B) If you increase the mass, what happens to the period?

C) If you increase the length, what happens to the period?

3) For a harmonic oscillator:

A) What is the formula for position over time? Sketch a graph.

B) What is the formula for velocity over time? Sketch a graph.

C) What is the velocity when the position is a maximum?

D) What is the position when the velocity is a maximum?

 

Solutions

Expert Solution


Related Solutions

1. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a...
1. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a state which is an equal mix of the ground state and the first-excited state. a) Write the time-dependent state in Dirac notation. b) Calculate 〈x〉. Calculate 〈p〉 using raising and lower operators. c) Graph 〈x〉 as a function of time.
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for...
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.) (a) What is the expectation value of position for this particle? (b) What is the expectation value of momentum for this particle? (c) What is ∆x for this particle? 2) Consider a harmonic oscillator potential. (a) If the particle is in the state |ψ1> =...
Consider a classical harmonic oscillator of mass m and spring constant k . What is the...
Consider a classical harmonic oscillator of mass m and spring constant k . What is the probability density for finding the particle at position x ? How does this compare to the probability density for the ground state of a quantum mechanical harmonic oscillator
1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the...
1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the spring constant is 6.6 N/m. The damping force is given by -b(dx/dt), where b = 220 g/s. The block is pulled down 12.4 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/8 of its initial value. (b) How many oscillations are made by the block in this time? 2.An oscillator consists of a block...
1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a...
1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a spring of spring constant 290 N/m. When t = 2.10 s, the position and velocity of the block are x = 0.141 m and v = 3.530 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? 2. If you took your pendulum to the moon, where the acceleration...
1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration....
1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration. (b) What does this approximation lack in terms of representing real molecular bonds? (c) When is the approximation most valid and when are higher order approximations necessary?
1) a) Establish schrodinger equation,for a linear harmonic oscillator and solve it to obtain its eigen...
1) a) Establish schrodinger equation,for a linear harmonic oscillator and solve it to obtain its eigen values and eigen functions. b) calculate the probability of finding a simple harmonic oscillator within the classical limits if the oscillator in its normal state.
1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation...
1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0cm. what is the oscillation frequency? 2. A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring? 3. An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The...
Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a...
Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a mass on a spring is given by ω=(k/m)1/2ω=(k/m)1/2 where m is the mass and k is the spring constant. The period of a harmonic oscillator is T=2π/ωT=2π/ω . If you do a little math, you can get a formula for the spring constant in terms of the mass and the period. a) Design a procedure to measure the spring constant based on Method A...
As in the figure below, a simple harmonic oscillator is attached to a rope of linear...
As in the figure below, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 ✕ 10−2 kg/m, creating a standing transverse wave. There is a 3.5-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.1 rad/s and an amplitude of 255.0 cm. (a) What is the distance between adjacent nodes? m (b) If the angular frequency of the oscillator doubles, what happens to the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT