Hello!
Now i need a bit explanation, so "oscillating circuit" capacitator + coil in series. Let's look at this as infinite, without any loss. We get changing magnetic field and electric field. Capacitator discharges, current goes to coil increasing its magnetic field, then starts magnetic field...
Hi,
First of all, I'm not sure at all how to start this question. I found the eigenvectors in a previous question, but I'm not sure if I need it to solve this one.
I think I need to use the expression for the position and velocity.
##a_n = C_n cos (\omega_n t + \alpha_n)##
##v_n = -\omega_n...
Hi,
First of all, I'm wondering if a beaded string is the right term?
I have to find the amplitude of the modes 2 and 3 for a string with 5 beads.
In my book I have $$A_n = sin(\kappa p)$$ or $$A_n = cos(\kappa p) $$ it depends if the string is fixed or not I guess. where $$\kappa = \frac{n\pi...
I'm trying to find the quality factor of a damped system.
I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)##
From this I found that ##T = \frac{\pi}{20}##
##\omega_d = \frac{2\pi}{T} = 40 rad##
Then, from the solution ##x(t) = A_0...
Hello there, I am wondering, in this solution, I guessed that the restoring force is given by that equation in the problem because the vertical component of the force acting on the ball is -2Tsin(x). since sin(x) = y/L with L being the hypotenuse part of the triangle formed by displacing the...
Hi,
I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass.
##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1)
##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2)
In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2##
I get...
Hi,
On a driving force graph ##y = displacement (m)## and ##x = time## where the external force start at t = 0 and the system is in equilibrium at x=0, it's easy to find the driving frequency.
$$F = \frac{\omega}{2\pi}, \omega = \frac{2\pi}{T}$$ and we can get ##T## easily with the steady...
T = 2π * √(2/300), T = .513 seconds.
If I divide it by 4/3, I get a final answer of .385 seconds of touch.
I know the box isn't attached for the entire oscillation, so T has to be divided. To me, it makes sense to divide it by 4/3 (when the box falls, the spring is compressed, hits...
I first found the equilibrium points taking the derivative of the potential. ##U'(x)=U_0 a\sin(ax)##, and the equilibrum is when the derivative is 0, so ##U_0 a\sin(ax)=0## so ##x=0## or ##x=\pi/a##. Taking the second derivative ##U''(x)=U_0a^2 \cos(ax)## I find that ##x=0## is a minimum point...
It is necessary to make a mechanism, the basis of which should be oscillation of the pendulum with an amplitude φ = 0.250 ± 0.002 rad. Is it possible to describe the motion of the pendulum to use a harmonic oscillator model?
How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0##
How...
I started off by finding when Fg=Fx:
(72)(x)=(31)(9.8)
x=4.2193m
After this I'm stuck and have a few things I'm confused about:
When the penguin's jumping, is there elastic energy? (because the rope's getting compressed? Or maybe not). Also, I know you can use energy conservation, but...
We know that the charge on capacitors as a function of time takes the general form of:
##Q(x,t)=qe^{ijka}e^{-i\omega t}##
The voltage at each capacitor:
##V_j = \frac 1 C (Q_j-Q_{i+1})##
From KVL we have differential equation of t-derivatives:
##LQ'' + RQ' = V_{j-1} - V_{j}##
##LQ''+RQ'= \frac...
How can I find omega on an object that is floating on water which is moving up and down on the object? The problem goes by giving you a cylindrical object with radius r and height H, pw(density of water), pc(density of circle) and x(t)=a*cos(wt). I do not understand why pw*pi*r^2*dg=pc*pi*r^2Hg
Homework Statement
a car moving to the left with constent accelration. a ball is hanging from the ceiling held in 90 degrees to the ceiling until t=0, then it is realesed and start to swing.
find the max angle.
Homework Equations
Newton's second law
The Attempt at a Solution...
Homework Statement
The system is shown in the image. In the beaded string shown in Figure 1, the interval between neighboring beads is a, and the distance from the end beads to the wall is a/2. All the beads have mass m and are constrained to move only vertically in the plane of the paper...
I know that I'm rushing too much but I wanted to see if I can calculate the work of a pendulum that does oscillation with a similar way you calculate the work of a spring. Consider the following free body diagram:
Things i noticed:
1) The position is changing both in x and y-axis while the...
Homework Statement
Is the time average of the tension in the string of the pendulum larger or smaller than
mg? By how much?
Homework Equations
$$F = -mgsin\theta $$
$$T = mgcos\theta $$
The Attempt at a Solution
I'm mostly confused by what it means by time average. However from my...
I need help with this question. The energy of wave related to its amplitude but not to frequency. If we talk about wave as disturbance carring energy we can imagine a swinging rope that gives potential energy to body by pushing it up. Bigger amplitude means getting high and increasing Potential...
What I understand about harmonics, is when something is transmitted at high power, the antenna resonates on other frequencies besides the desired one. But Why?
Homework Statement
How can I calculate the initial phase in a simple harmonic motion if I only have the amplitude, frequency and angular velocity as data?
Homework Equations
The formula of the position, in fact they ask me to do the formula that allows to know the elongation depending on the...
Homework Statement
A tuba is a instrument that can be modeled after a closed tube and has a length of 4.9m. A frequency of 122.5hz produces resonance in the Tuba. Is this the fundamental frequency of the instrument? If not, what harmonic is it?
Homework Equations
f=λv
4l=λ(open closed tube)
v=...
Homework Statement
A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator:
H = \hbar \omega (a_+ a_- + \frac{1}{2})
at t = 0 we have
\Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x))
Find the expectation value and variance of harmonic oscillator...
Homework Statement
The figure shows a uniform thin rigid plank of length 2b which can roll
without slipping on top of a rough circular log of radius a. The plank is initially
in equilibrium, resting symmetrically on top of the log, when it is slightly
disturbed. Find the period of small...
I observed something which I've never seen before. We left the tap open and the water stream was flowing in a particular pattern. When we placed a beaker under the water stream, the pattern disappeared. And the pattern itself was oscillating.
Here's the video link.
Below the the photos of the...
Homework Statement
A solid cylinder of mass, M, is connected to two springs of total stiffness, k. The springs are connected tangentially (on top) to the cylinder. The other ends of the springs are attached to walls. What is the period of oscillation of the cylinder assuming that it does not...
1.
A mass, M = 1.61 kg, is attached to a wall by a spring with k = 559 N/m. The mass slides on a frictionless floor. The spring and mass are immersed in a fluid with a damping constant of 6.33 kg/s. A horizontal force, F(t) = Fd cos (ωdt), where Fd = 52.5 N, is applied to the mass through a...
Homework Statement
The acceleration amplitude of a damped harmonic oscillator is given by
$$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$
Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}##
Homework Equations
$$\it{R}(\omega) =...
Homework Statement
You got a plate hanging from a spring (hookes law: k) with a viscous force acting on it, -bv.
If we place a mass on the plate, gravity will cause it to oscillate.
Prove that if we want the plate to oscillate as little as possible (Crticial damping, no?), then $$b=2m...
1. Problem Description:
A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest at a position y. The object is then released from y and oscillates up and down, with its lowest position being 10cm below y.
What is the frequency...
Homework Statement
I'm currently working on the "cavendish" experiment and wish to use/develop a method separate from the casus we've been provided. Now I've nicely calculated and derived everything I need to know, including all the corrections that have to be made for the mass of the rod, the...
Homework Statement
An oscillator is attached to one end of a horizontal string. The other end passes over a frictionless pulley and is held taught by a mass m. The distance between the oscillator and the pulley is 1.2m. The string has a linear mass density of 1.6g/m and the frequency of the...
Homework Statement
A mass "m" is attached to a spring of constant "k" and is observed to have an amplitude "A" speed of "v0" as it passes through the origin.
a) What is the angular frequency of the motion in terms of "A" and "v0"?
b) Suppose the system is adjusted so that the mass has speed...
To increase the period of oscillation of a pendulum in 1 second, it is needed to increase the length of it in 2 meters. Calculate, in seconds, of the initial period of oscillation of the pendulum.
I found this question online a few minutes ago. I have not learned this in physics class yet so...
You have an infinitesimally small mass in the center of octahedron. Mass is connected with 6 different springs (k_1, k_2, ... k_6) to corners of octahedron.
Equilibrium position is in the center, you don't take into account gravity, only springs.
Find normal modes and frequencies.
Relevant...
A spring of spring constant k sits on a frictionless horizontal table, one end of the spring is attached to a wall the other end to a block of mass M= 2kg, also resting on the frictionless table. Another block of mass m=450g moving at a speed of 7m/s collides in-elastically with the block of...
Homework Statement
A little amount of sand is spilt over horizontal membrane that oscillates with frequency f=500Hz in vertical plane. If sand grains are jumping to the height h=3mm with respect to the equilibrium position, find amplitude of oscillation of membrane.
Homework Equations
ω=2πf...
Homework Statement
There's a horizontal thin wire whose mass is negligible and whose length is l=1m. It is strained with constant force F=10N. If we place a tiny pellet in the middle of wire (mass of pellet is m=1g) and then we bring wire out of equilibrium position (moving out of it's original...
Homework Statement
I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)##
Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ##
The attempt at a...
Homework Statement
Point with mass is moving along the positive direction of x axis, its velocity is described by (A-Bx^2)^(1/2). Show that its equation of motion describes dynamic harmonic oscillation and find period (T) of this oscillation.
Homework Equations
v=(A-Bx^2)^(1/2)
A and B is...
The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time.
For example, if I have
x'' + ω02x = cos(ωt)
If we suppose that ω≠ω0,
then the general solution should look something like:
x(t) = c1cos(ω0t) + c2sin(ω0t)...
Awhile back, I was learning about springs, and restoring/distorting force. We even did an experiment where we hung a spring and put weights on it and pulling it down, watching it oscillate.
From this, I assumed the distorting force was the force that stretched the spring and restoring force is...
Homework Statement
Use the Heun method to compute the period of small oscillations about the equilibrium position of a nitrogen atom.
xi = 1.1
Um = 7.37
x0 = 1.2
alpha = 2.287
m = 2.325e-26
Homework Equations
[/B]
U(x) = Um((1-e^(-alpha(x-x0)))^2 - 1)
The Attempt at a Solution
I was told to...
I bought a PH meter with glass electrode. I calibrated it using a buffer solution following the instructions.
When I measure the PH of tap water, vinegar, or other simple liquids it initially keeps changing but eventually it stabilizes at the correct value. But I tried to measure gastric juice...
Homework Statement
A rod of length ##2L## is bent at point of its middle so that the rods now created are in a upside V shape and the angle between them is ##120°##. The system oscilates. Find the expression of the period of oscilation.
Homework Equations
3. The Attempt at a Solution [/B]
I...
Homework Statement
Water waves in a shallow dish are 6.0 cm long. At one point the water oscillates up and down at a rate of 4.8 oscillations per second.
a. What is the speed of the water waves?
b. What is the period of the water waves?
Homework Equations
frequency = 1/period
Speed =...
Hi, I'm having some problems to complete this problem if some body can explain me the points c an d... ;)
An object with 1.5 kg mass located on a spring with constant of 600 N/m oscillates so that the amplitude decreases 3%in each cycle. Subsequently, the system is driven with a sinusoidal...
Homework Statement
A 75 gram ruler is evenly placed between two cylinders spinning clockwise on the left and counter clockwise on the right. The coefficient of friction between the ruler and the spinning cylinders is 0.2. You push the ruler to the right by 0.12 meters. It returns to you by...