Homework Answers
clc;clear all;
k1=2;
k2=5;
k3=4;
P=50;
f=@(x)
0.5*k2*x(1)^2+0.5*k3*(x(2)-x(1))^2+0.5*k1*x(2)^2-P*x(2);
A=[-1 2];% inequalities being defined as Ax<=b,where A is vector
of coefficients
b=5;
x0=[1 1];%initial value of x1 and x2
x=fmincon(f,x0,A,b);
x1=x(1)
x2=x(2)
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Question 1 130 pts Jmincon function to find the minimum value of the potential energy PE of follo...
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Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
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Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
We consider here, the two masses m1 and m2 connected this time by springs of stiffnesses...
We consider here, the two masses m1 and m2
connected this time by springs of stiffnesses k1,
k2 and k3 as shown in the figure below. We
denote by x1(t) and x2(t) the movement of
each of the 2 masses relative to its position of equilibrium
static.
1. Prove that the differential equation whose unknown is the
displacement x1(t) is written in the following form: (3
points)
2. Deduce the second differential equation whose unknown is the
displacement x2(t) (3...
We consider here, the two masses m1 and m2 connected this time by springs of stiffnesses...
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as shown in the figure
below. We denote x1 (t) and x2 (t) as the movement of each of the 2
masses relative to its position of equilibrium static.
1) Prove that the differential equation whose unknown is the displacement is written in the following form:
2) Deduce the second differential equation whose unknown is the
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3) Determine the...
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Question 1 1 pts Given the following Potential Energy function with depends on the position , PE (k/2) x3 what is the force in the x direction? O F (3 k/2) x2 O F-(k/2) x2 O F(3 k/2) x2
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Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
We consider here, the two masses m1 and m2
connected this time by springs of stiffnesses k1,
k2 and k3 as shown in the figure below. We
denote by x1(t) and x2(t) the movement of
each of the 2 masses relative to its position of equilibrium
static.
1. Prove that the differential equation whose unknown is the
displacement x1(t) is written in the following form: (3
points)
2. Deduce the second differential equation whose unknown is the
displacement x2(t) (3...
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as shown in the figure
below. We denote x1 (t) and x2 (t) as the movement of each of the 2
masses relative to its position of equilibrium static.
1) Prove that the differential equation whose unknown is the displacement is written in the following form:
2) Deduce the second differential equation whose unknown is the
displacement
3) Determine the...
Question 1 1 pts Given the following Potential Energy function with depends on the position , PE (k/2) x3 what is the force in the x direction? O F (3 k/2) x2 O F-(k/2) x2 O F(3 k/2) x2
Finite element method
A) Total potential energy of a spring system Write the expression for the total potential energy of the spring system below 11 ki 43 1lg ii) Specify the boundary conditions B) Shape function and its properties i) Write the expression for the shape function matrix N- [N(C) N,(o)] and strain- !-[ dN displacement matrix B=|ー1 for a typical two-node linear trusbar element shown dx below N, (x) = N, (x) x,-x, x2-XI x1 Element 1 Node 2...
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1.
2.
Question 10 1 pts The graphs show potential energy diagrams for the same reaction at T-900. K R P 1) uncatalysed process; 2) catalysed reaction Uncatalyzed Reaction 400 300 reactants 200 100 products Reaction coordinate Uncatalysed reaction: Potential Energy (P.E.) vs reaction coordinate. Energy is measured from O to 400. kJ, and the reaction coordinate is associated with the evolution of the reaction. The PE of the reactants is 225 kJ. Then the energy grows to 400. kJ,...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
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(a) Evaluate an expression for the expectation value of the potential energy for the n 3, 1-1, m = 1 wavefunction of the hydrogen atom. You need to compute the integral, where e2 [4 marks] 0 wave- 6 marks] [2 marks] Write the answer in terms of h. e and me (b) Calculate the expectation value of the kinetic energy for the n-1,- function of the hydrogen atom....
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