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The total energy for the vibrating string problem can be written...
1. The total kinetic energy of the vibrating string is given by the integral (a) Why...
1. The total kinetic energy of the vibrating string is given by the integral (a) Why does this integral give kinetic energy? (b) The potential energy V(t) of a stretched string originates in the work done against the tension T when as a result of its displacement, the string becomes longer. Show that (c) Use the series expression (3.16b if Nettel) to show that the total energy can be written as a sum over normal mode terms, with no cross-terms...
Consider a uniform string of length 1, tension T, and mass per unit length p that...
Consider a uniform string of length 1, tension T, and mass per unit length p that is stretched between two immovable walls. Show that the total energy of the string, which is the sum of its kinetic and potential energies, is E = EST-C3) + ) dx. where y(x, t) is the string's (relatively small) transverse displacement.
Need help with this problem. BC 1. Solve the vibrating string problem PDE Uz = 4uzz...
Need help with this problem.
BC 1. Solve the vibrating string problem PDE Uz = 4uzz uz(0,t) = 0 ВС uz(1,t) = 0 IC u(a,0) = cos(372) (3,0) = r 0<x< 1, 0 <t< oo 0<t< 0<t<oo 0<x<1 0<x<1. IC
The vibrating string problem is given by the equations below. Solve this problem with α-2L and th...
The vibrating string problem is given by the equations below. Solve this problem with α-2L and the initial functions f(x-7 sin 8x + 19 si 10x and a x-0. Ul 0<x<L,t0 t2 0 t2 0 ot u(x,0) f(x) 0sxSL du u(L,t) = 0 u(x,t) = X Sorry, that's not correct. Sorry, your answer is not correct. Correct answer: 4 cos (21t) sin (7x)+17 cos (30t) sin (10x) Your answer a Similar Question Next Question
The vibrating string problem is given...
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the s...
parts a,b, c
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the string is initially at rest. The initial boundary value problem (IBVP) is written as u(0,t) -u(1,t) u(x,0) = f(x), 0 ut (z, 0-0, 0 < x < 1. The solution of this IBVP using the method of separation of variables is given by n-l a) Find the coefficients bn. b) Show that this wave function can be written as the...
Please help me with this 1D vibrating string problem. That has a Dirichlet boundary condition at...
Please help me with this 1D vibrating string problem. That has a
Dirichlet boundary condition at both ends and the string is at rest
when t=0.
Picture on the equation below
What is missing for this to be solved? Please elaborate
htt(t, x)=c2hxx(t, x) + f sin(vt), x E [0, π].
please show work, thank you. Question #4: (25 points total) In this problem, you are going...
please show work, thank you.
Question #4: (25 points total) In this problem, you are going to walk you through a brief history of quantum mechanics apply the principles of quantum mechanics to a physical system (free electron) 1900 Planck's quantization of light: light with frequency v is emitted in multiples of E hv where h 6.63x10-341.s (Planck's constant), and h =hw h 1905 Einstein postulated that the quantization of light corresponded to particles, now called photons. This was the...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0 u(1,t0 u(x,0cos(3T) 14(2.0) = x
Partial Differential Equation - Wave equation : Vibrating spring Question 2 A plucked string, Figure 2 shows the initial position function f (x) for a stretched string (of length L) that is set in mot...
Partial Differential
Equation
- Wave equation : Vibrating spring
Question 2 A plucked string, Figure 2 shows the initial position function f (x) for a stretched string (of length L) that is set in motion by moving t at midpoint x =-aside the distance-bL and releasing it from rest timet- 0. f (x) bL Figure 2 (a) If the length of string is 10cm with amplitude 5cm was set initially, state the initial condition and the boundary conditions for the...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be mode...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be modeled by -27- 0<r<T, t>0 (PI) u(0, t) = u(, t ) t20 0 is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign. (2 points) (4 points) (b) Consider the separable solutions to (P1), ie., those of...
1. The total kinetic energy of the vibrating string is given by the integral (a) Why does this integral give kinetic energy? (b) The potential energy V(t) of a stretched string originates in the work done against the tension T when as a result of its displacement, the string becomes longer. Show that (c) Use the series expression (3.16b if Nettel) to show that the total energy can be written as a sum over normal mode terms, with no cross-terms...
Consider a uniform string of length 1, tension T, and mass per unit length p that is stretched between two immovable walls. Show that the total energy of the string, which is the sum of its kinetic and potential energies, is E = EST-C3) + ) dx. where y(x, t) is the string's (relatively small) transverse displacement.
Need help with this problem.
BC 1. Solve the vibrating string problem PDE Uz = 4uzz uz(0,t) = 0 ВС uz(1,t) = 0 IC u(a,0) = cos(372) (3,0) = r 0<x< 1, 0 <t< oo 0<t< 0<t<oo 0<x<1 0<x<1. IC
The vibrating string problem is given by the equations below. Solve this problem with α-2L and the initial functions f(x-7 sin 8x + 19 si 10x and a x-0. Ul 0<x<L,t0 t2 0 t2 0 ot u(x,0) f(x) 0sxSL du u(L,t) = 0 u(x,t) = X Sorry, that's not correct. Sorry, your answer is not correct. Correct answer: 4 cos (21t) sin (7x)+17 cos (30t) sin (10x) Your answer a Similar Question Next Question
The vibrating string problem is given...
parts a,b, c
Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the string is initially at rest. The initial boundary value problem (IBVP) is written as u(0,t) -u(1,t) u(x,0) = f(x), 0 ut (z, 0-0, 0 < x < 1. The solution of this IBVP using the method of separation of variables is given by n-l a) Find the coefficients bn. b) Show that this wave function can be written as the...
Please help me with this 1D vibrating string problem. That has a
Dirichlet boundary condition at both ends and the string is at rest
when t=0.
Picture on the equation below
What is missing for this to be solved? Please elaborate
htt(t, x)=c2hxx(t, x) + f sin(vt), x E [0, π].
please show work, thank you.
Question #4: (25 points total) In this problem, you are going to walk you through a brief history of quantum mechanics apply the principles of quantum mechanics to a physical system (free electron) 1900 Planck's quantization of light: light with frequency v is emitted in multiples of E hv where h 6.63x10-341.s (Planck's constant), and h =hw h 1905 Einstein postulated that the quantization of light corresponded to particles, now called photons. This was the...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0 u(1,t0 u(x,0cos(3T) 14(2.0) = x
Partial Differential
Equation
- Wave equation : Vibrating spring
Question 2 A plucked string, Figure 2 shows the initial position function f (x) for a stretched string (of length L) that is set in motion by moving t at midpoint x =-aside the distance-bL and releasing it from rest timet- 0. f (x) bL Figure 2 (a) If the length of string is 10cm with amplitude 5cm was set initially, state the initial condition and the boundary conditions for the...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be modeled by -27- 0<r<T, t>0 (PI) u(0, t) = u(, t ) t20 0 is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign. (2 points) (4 points) (b) Consider the separable solutions to (P1), ie., those of...
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