Equation of motion Definition and 266 Threads

I have a question to a physical task in Mathematica. We have this equation of motion: For energy of masspoint there is the condition : I have to write a procedure that uses the law of the conservation of energy for the potential V(x) to calculate t(x_1) - t(x_0) when there are given two...

Homework Statement ##\ddot{\Phi_i}-\frac{k}{ml^2}\Phi_i+\frac{k}{ml^2}\Phi_{i+1}=0## This is the equation of motion of a series of pendulums linked by a torsion spring in the case where ##g=0## Homework EquationsThe Attempt at a Solution I haven't really met this type of equation before. I...

Homework Statement ##\ddot{r} = c \frac{1}{r^2}##, where ##c## is a constant, and ##r## is the position of one object with respect to the other. I need to find the function ##\dot{r}(r)## We are in one dimension. Homework EquationsThe Attempt at a Solution I don't really have any idea how to...

So if you have a rocket let's say that discards all the structural and engine mass continuously at zero velocity that is relative to the rocket until only the payload is traveling at the final velocity - then what will the equation of motion will look like? we can neglect the drag and...

I'm having trouble understanding the forces involved when defining the equation of motion for this particular problem. So... I've seen the answer for the eq. of motion worked two different ways. The first way involves combining the spring series into Keq = K1⋅K2/(K1+K2). The answer, plugging...

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

Let's consider a particle moving along x – axis, its position at t = 1s is 1m and speed is 1 m/s. How can one calculate acceleration on the basis of this information?

Homework Statement :[/B] Say for example I've got the equation of a SHM as: $$x = A \cos (\omega t + \phi)$$ where ##A## is the amplitude. How do I find the time period of this motion? Homework Equations :[/B] Stated above. The Attempt at a Solution :[/B] I tried by finding the second...

Homework Statement from the lagrangian density of the form : $$L= -\frac{1}{2} (\partial_m b^m)^2 - \frac{M^2}{2}b^m b_m$$ derive the equation of motion. Then show that the field $$F=\partial_m b^m $$ justify the Klein_Gordon eq.of motion. Homework Equations bm is real. The Attempt at a...

Homework Statement This problem showed up in my final review packet, and I /think/ it should be basic kinematics, but I don't even know how to approach it with the second half of it. An object moves according to the equation x = vt + ke^(bt), where k, v, and b are constants, x represents...

Vibrations - Modelling system, equation of motion Hi, In the first question (question 4) in the attached file, how would you go about modelling the system and finding the equation of motion? All those masses are confusing me, I don't even know where to start. I don't know whether the angle...

Hello everybody, I Am Meaningless and I had this doubt when I was reading some illustrations based on questions in Particle mechanics. So the Question was, A particle is attracted by a force to a fixed point varying inversely as (distance)^n. If the velocity acquired in falling from an...

See attached photo please. So, I don't get how equations of motion derived. Why is it that x dot is partial derivative of H in term of p but p dot is negative partial derivative of H in term of x.

Homework Statement I am not looking for a solution to the problem, as much as I need a clarification on what it's asking for. The problem: "A particle of mass m slides down an inclined plane under the influence of gravity. The particle is starting its motion from rest. Find the time dependence...

Hi, I have a Driving wheel for which I'm trying to make an observer for. The abserver works very well however , since I don't have my background in mechanics something strange happens. I have to say that I don't know why I think it's strange and that's why I put my question here. Lets assume we...

My question is that how does the Schrodinger equation arise from the Heisenberg equation of motion in the quantum field formalism. These are from Hatfield's book. So I'm having some difficulties to reproduce (2.36) by plugging (2.55) into (2.37) primarily because H is an integral...

Is the attached solution complete? In particular, do we need to prove that ##V'(r_{12}')=V(r_{12})##, where ##V'(r_{12}')## is the potential energy function in the reference frame ##S'##, moving at a uniform velocity with respect to the reference frame ##S##, and ##r_{12}'## is the distance...

Homework Statement Andy Roberts the former West Indian Cricket player and Fast Bowler, bowled his fastest delivery in 1975 at 159.5 km/h. Neglecting air resistance, calculate the maximum distance he could have thrown the ball at this speed (on earth!) had he been able to throw it: i)...

Homework Statement Hi, I have the following question... A pendulum consisting of a mass of 1kg is suspended from a string of length L. Air resistance causes a damping force of bv where b = 10-3 N/m 1) Derive and solve the equation of motion 2) Calculate the fractional decrease in amplitude...

Hi, I've derived the equation of motion for a regular single pendulum, but do not know how to solve the differential equation. I have the following: r2θ''2=mg(cosθ-rsinθ)

Homework Statement I think I made a mistake somewhere.. Homework Equations T = Jα T = F*R The Attempt at a Solution A) I started with T = Jα Since there is no slip, αm = αL Thus: Tm / Jm = TL / JL Plugging in, we find TL = Tm * JL / Jm = 2560 Now use T = F*R. Tm = Fm * Rm Plugging in...

"historically the Heinsenberg equation of motion was first written by P. A. M Dirac, who - with his characteristic modesty- called it the Heinsenberg equation of motion." Modern quantum mechanics/ J.J. Sakurai, page 84 Why dirac did that?, I didn't find any source. Any information about this...

[Mentor's note : No template as this thread was moved from the technical forums] Hi all! I am working on finding the Lagrangian for the situation stated in the title. This is actually a Wolfram Mathematica demonstration as well in which they give you the Lagrangian. I am working on re-deriving...

Is there any deep reason behind this? per example the principle of least action or something else?

Homework Statement derive the equation of motion of a mass-spring-pulley system using lagrange's equations. A mass m is connected to a spring of stiffness k, through a string wrapped around a rigid pulley of radius R and mass moment of inertia, I. Homework Equations kinetic energey T = 1/2...

Homework Statement Hello PF, I need some help with the assignment given: v=18-2t^2 m/s, where t is in second. When t= 0 the position of the particle is s_0 = - 3 m. For the first 5 seconds. Determine the total distance ( i got it to 65,33 ft) and the net displacement Δs, and the value of s at...

From the equation of motion of inflation, $$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + \frac{dV}{d\phi} = 0$$ Example: ##V= \frac{1}{2}m^2\phi^2## $$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + m^2\phi = 0$$ If I want to make the DE dimensionless then I let ##~t = \frac{1}{H_o} \tilde t~## and...

Homework Statement To find the period of oscillation of the pendulum and the equation of motion. Homework Equations Conservation of energy. Potential energy in a constant field = mgh. Kinetic energy in polar coordinates with r constant = (1/2) m r2 (dΘ2/dt2) The Attempt at a Solution I won't...

Hallo, I Wonder how i can get the equation of motion for a tilting Stick of mass M and lengh L with an additional mass m placed in it in distance of l from the Center of rotation. I thought about the moments of inertia Can anybody help? Thanks in advance

A flying object is moving in 3D space having translational velocity and the object is also rotating. Consider a body frame (xb-yb-zb) attached to the C.G of the moving body. Hence the body attached frame is also translating and rotating (as the object is flying) with respect to a fixed inertial...

Homework Statement A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...

Homework Statement My professor posted this problem on his page as a self-assessment for the students and said that you just need some analytical geometry notions and trigonometry to solve it, although I don't quite get how to solve it. This is the problem statement: Considering the articulated...

Homework Statement Find the equation of motion of the object by setting the derivative of the total energy equal to zero. Homework Equations r(theta)=(Rcos(theta), Rsin(theta), q*theta) v(theta)=dr/dt=(-Rsin(theta)dtheta/dt, Rcos(theta)dtheta/dt, q*dtheta/dt) derivative of Total Energy =...

Homework Statement A small block of mass m is suspended from the top of a box by a mass-less string of length L. Two identical springs, each with spring constant k, extend from the block to the sides of the box, as shown in the diagram to the right. The length of the springs is such that they...

a particle of mass m is projected towards a point O with initial speed √5/3 m/s from a point P where [OP]=3 metres. the particle is repelled from O by a force of magnitude 4m/x³ where x is its distance from O. (i) show that the equation of motion is v dv=4x^-3 dx (ii) find how close the particle...

Homework Statement Hi everybody! I'm a bit stuck in this problem, hopefully someone can help me to make progress there: A mass point ##m## is under the influence of a central force ##\vec{F} = - k \cdot \vec{x}## with ##x > 0##. a) Determine the equation of motion ##r = r(\varphi)## for the...

The Schwarzschild equation of motion, where coordinate length is differentiated by proper time is as far as I know r''(t) = -\frac{G\cdot M}{r(t)^2} + r(t)\cdot{\theta}'(t)^2 - \frac{3\cdot G\cdot M\cdot{\theta}'(t)^2}{c^2} {\theta}''(t) = -2\cdot r'(t)/r(t)\cdot{\theta}'(t) Now the question...

Hi, i am an student of civil engineering and i am doing my graduate thesis. so sorry if i misspell, english is not my native languaje. so, here we go :D Homework Statement Before entering in details you (whoever you are) most know: The system is scaled for obvious reasons. The system consists...

Consider the 1d motion of a body under the influence of the force given by F = -m*γ*vα. m is mass, γ is a constant of appropriate dimension, v is velocity and α is dimensionless constant. The value of α for which the motion will come to a stop in finite time is to be calculated. I solved the...

Homework Statement Hi everybody! I'm stuck at a problem I was given in my special relativity theory class, can anybody help? A golfer is on the North Pole, on a flat surface perpendicular to the Earth axis and without friction. He places himself at distance L from the pole and hits the ball...

Homework Statement As part of a problem, I need to derive the EOM for a generalized Lagrangian. Before I get there, I'm trying to refresh myself on exactly how these derivatives work because the notation is so bizarre. I am trying to follow a simple example I found online: Start with...

Homework Statement I must find the following equation of motion: φ'' + 3Hφ' + dV/dφ = 0 Using the scalar field Lagrangian: (replace the -1/2m^2φ^2 term with a generic V(φ) term though) with the Euler-Lagrange Equation I know that I must assume φ = φ(t) and the scale factor a = a(t)...

Homework Statement A string of length ##a##, mass per unit length ##\sigma## and under tension ##T## is fixed at each end. The Lagrangian governing the time evolution of the transverse displacement ##y(x, t)## is ##L = \int_{0}^{a} dx \bigg[ \frac{\sigma}{2} \Big( \frac{\partial y}{\partial...

Hello, I am having trouble deriving the equation of motion for the quintessence field. The equation of motion which I am meant to get at the end point is: (with ' denoting derivative w.r.t time) φ'' + 3Hφ' + dV/dφ = 0 Using the inflaton lagrangian: (although with a generic potential V(φ)...

I had seen a documentary about an algorithm that uses notions of evolution to deduce the equation of motion of a system by sampling a variable connected with the system. For example, they used the double pendulum case where they sampled the position of the free end of the pendulum and arrived...

Dear All I am trying to find the equation of motion of the spin connection out of the einstein hilbert action written in terms of the vielbeins. Can anyone help me to do? Thank you

When we apply this equation ? v^2-u^2=kt^2/2m

Setting a cartesian system how can i get the equation of the trajectory of an object knowing the forces acting on that object? Example: If F= GMm/r^2 and let be the sun at the center (point (0,0,0)) of the cartesian system how do i get the equation of an ellipse in this system? ( x^2/a^2 +...

Hi all, I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed. To obtain...

Homework Statement A projectile is launched horizontally with an initial velocity v0 from a height h. If it is assumed that there is no air resistance, which of the following expressions represents the vertical trajectory of the projectile? (A) h–gv0^2/2x^2 (B) h–gv0^2x^2 (C) h-gx^2/2v0^2 (D)...