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 above. Describe your experimental procedure in the text box below.

b) Now, describe the mathematical procedure you will use to calculate the spring constant based on your measurements.

c) Your mathematical procedure above represents a mathematical model of an oscillating mass. What assumptions and idealizations were made in this model? Discuss how these assumptions might affect the outcome of your experiment.

Expert Solution

genius_generous answered 2 years ago

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental...

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental phase difference φ. And constant spacing d between them. The total length of the array of the oscillator is L. With L = N*d The amplitude is: where A0 the amplitude of each wave. A = A0 sin(Nφ /2) / sin(φ /2) The intensity : I = I0*(sin(Nφ /2) / sin(φ /2))^2 1. show the minimum is at Nd*sin(θ ) = m λ, m...

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...

a) a simple harmonic oscillator consists of a glass bead attached to a spring. it is...

a) a simple harmonic oscillator consists of a glass bead attached to a spring. it is immersed in a liquid where it loses 10% of its energy over 10 periods. compute the coefficient of kinetic friction b assuming spring constant k=1 N/m and mass m=10 grams; b) suppose the spring is now disconnected and the bead starts failing in the liquid, accelerating until it reaches the terminal velocity. compute the terminal velocity.

Show that, in a symmetrical 2D linear harmonic oscillator, the expectation value for total angular momentum...

Show that, in a symmetrical 2D linear harmonic oscillator, the expectation value for total angular momentum is conserved with time.

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is...

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is . What is the displacement of the mass at 2.2 seconds? ___________m What is the spring constant? ___________________N/m What is the position of the object when the speed is maximum? ______________m What is the magnitude of the maximum velocity?____________________m/s

Solve the quantum harmonic oscillator problem by using the matrix method.

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...

A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring...

A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring of spring constant 260 N/m. When t = 1.60 s, the position and velocity of the block are x = 0.199 m and v = 3.920 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?

A simple harmonic oscillator consists of a 0.63 kg block attached to a spring (k =...

A simple harmonic oscillator consists of a 0.63 kg block attached to a spring (k = 190 N/m). The block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total mechanical energy of 6.0 J. (a) What is the amplitude of the oscillation? (b) How many oscillations does the block complete in 12 s? (c) What is the maximum kinetic energy attained by the block? (d) What is the speed of the block at...

Question