Related questions
Consider the Lennard-Jones potential between atoms of mass m in a solid material.c) Consider two neighbouring atoms subject to the Lennard-Jones interaction as above. An
experimentalist applies an external driving force F = F0cos(ωt) to separate and bring to-
gether the atoms.
Write down the differential equation describing the motion of the atoms and determine the
amplitude of the oscillations as a function of ω0, F0 and m. You may assume that this is
after sufficient time so that you may ignore any transient solutions.
d). A further interaction is added that introduces friction to the system so that there is now a
friction force −c
dr
dt , where r is the atomic separation.
Write down the differential equation and solve it to determine the amplitude in terms of the
coefficients in the differential equation. You may assume that this is after sufficient time so
that you may ignore any transient solutions.
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- As shown in the figure below,a small ball of mass m is attached to the free end of an ideal string of length 7 that is hanging from the ceiling at point S. The ball is moved away from the vertical and released. At the instant shown in the figure, the ball is at an angle ✪ (t) with respect to the vertical. Suppose the angle is small throughout the motion. zero of potential g pivot S 1 marrow_forwardThe system composed of two springs and a particle with mass ? shown in the figure can beconsidered as a system with a single equivalent spring. Suppose you move the particle and stretchboth springs (since the force constants are not the same, it cannot be assumed that both springs arestretch the same, you must find a relationship between how much each spring stretches and the displacement of the spring.particle). Determine an expression for the equivalent spring constant in terms of the constantsof each spring.arrow_forwardProblem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let la be the length of the spring at equili brium, and r be the elongation. The block oscillates and at the same time is rotating around origin 0, in the plane of the inclined, by a variable angular velocity . 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) k reference plane m o'arrow_forwardI'm doing calc1 by myself right now and not sure where to start with this problem: Here are the questions: An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)*100sin(x)-10cos(x))/101 *(See photo i have provided)* a) Give the object movement for the first 10 seconds. I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant b) Give the total distance traveled by the object during the first 10 seconds I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them? c) Give the total distance that will be traveled by the object from time t = 0. at this point i am clueless to what i should find I…arrow_forwardConsider the system below with physical parameters M = 1.3, K1 = 7, K2 = 3, g = 9.81 a) Develop the dynamic equations using the Lagrangian approach b) Explain which are the potential forces of this systemarrow_forwardarrow_back_iosarrow_forward_ios