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Problem 3. Rising Snake A snake of length L and linear mass density p rises from...
2. The dispersion relation for oscillation of a string (It has a length L with linear mass density μ and under tens...
2. The dispersion relation for oscillation of a string (It has a length L with linear mass density μ and under tension T is given by: α is a positive constant. The string is fixed at x-0 and x-L. At t:0 The sting displacement is given by: (a) (10 points) Find the phase velocity (b) (10 points) Find the group velocity (c)(7 points) What are the frequencies of the normal modes (d) (3 points) at what time t will the...
8.9.) A chain of mass m and length l lies on a horizontal table with a...
8.9.) A chain of mass m and length l lies on a
horizontal table with a portion hanging over the edgeof the table.
The only force acting on the system is the constant gravitational
force in the negative y- direction. Set up and solve Lagrange's
equation. Assume uniform mass density.
8.10.) a) Set up Lagrange's equations for the double pendulum
(Figure 8.8).
b) Assume that the amplitudes are very small. Simplify the
equations keeping only terms linear in the variables....
Given a linear mass density of A(L-x), find the mass and center of mass from the...
Given a linear mass density of A(L-x), find the mass and center of mass from the left end of a thin rod of length L J.
Please answer Q1 and Q2!!! Golf Club: Driver shaft has length L Neglect its mass to...
Please answer Q1 and Q2!!!
Golf Club: Driver shaft has length L Neglect its mass to simplity problem. Driver head is a sphere of uniform density with mass M and radio's R. Golf Ball: Ball is a uniform sphere of mass in and radius r. Initial relucity of driver head V = (vi, 0,oo What is the initial angular relacity of the driver head to in terms of vi, L, and R? Initial relaty of golf ball Tej = 0...
A wooden board of length L and total mass m has a linear mass density λ...
A wooden board of length L and total mass m has a linear mass density λ = α x3. • A.) Find the constant α in terms of L and m. • B.) Find the center of mass of the board in terms of the given algebraic variables. Assume the left end of the board is placed at x = zero. • C.) If the pivot point is placed at the center of the board and a block of mass...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current I = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al)....
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density 1...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density 1 are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current / = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
Homework problem: Given a string fixed at both ends of length L and linear density el....
Homework problem: Given a string fixed at both ends of length L and linear density el. The string is plucked from a height h, 1/4 of the distance from the end initial velocity of all parts of the string is zero): Part 2a (20 pts): What is the equation of motion y(x,t) for this system? 01/4L Part 2b (20pts): given the trial solution y(x,t) = 2n=o(An cos(wnt) + B, sin(wnt))sin (knx), what are the values of An and Bn.
Problem 5: A cord with length L 2 m has a ball of mass m 1...
Problem 5: A cord with length L 2 m has a ball of mass m 1 kg attached to the end. The ball is released from rest, when the cord makes an angle of 30° with the vertical. 1) How much work does the gravitational force do on the ball from A to B? 2) What is the speed of the ball at point B? 3) What is the tension in the cord at point B? 4) What initial velocity...
2. The dispersion relation for oscillation of a string (It has a length L with linear mass density μ and under tension T is given by: α is a positive constant. The string is fixed at x-0 and x-L. At t:0 The sting displacement is given by: (a) (10 points) Find the phase velocity (b) (10 points) Find the group velocity (c)(7 points) What are the frequencies of the normal modes (d) (3 points) at what time t will the...
8.9.) A chain of mass m and length l lies on a
horizontal table with a portion hanging over the edgeof the table.
The only force acting on the system is the constant gravitational
force in the negative y- direction. Set up and solve Lagrange's
equation. Assume uniform mass density.
8.10.) a) Set up Lagrange's equations for the double pendulum
(Figure 8.8).
b) Assume that the amplitudes are very small. Simplify the
equations keeping only terms linear in the variables....
Given a linear mass density of A(L-x), find the mass and center of mass from the left end of a thin rod of length L J.
Please answer Q1 and Q2!!!
Golf Club: Driver shaft has length L Neglect its mass to simplity problem. Driver head is a sphere of uniform density with mass M and radio's R. Golf Ball: Ball is a uniform sphere of mass in and radius r. Initial relucity of driver head V = (vi, 0,oo What is the initial angular relacity of the driver head to in terms of vi, L, and R? Initial relaty of golf ball Tej = 0...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current I = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density 1 are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current / = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
Homework problem: Given a string fixed at both ends of length L and linear density el. The string is plucked from a height h, 1/4 of the distance from the end initial velocity of all parts of the string is zero): Part 2a (20 pts): What is the equation of motion y(x,t) for this system? 01/4L Part 2b (20pts): given the trial solution y(x,t) = 2n=o(An cos(wnt) + B, sin(wnt))sin (knx), what are the values of An and Bn.
Problem 5: A cord with length L 2 m has a ball of mass m 1 kg attached to the end. The ball is released from rest, when the cord makes an angle of 30° with the vertical. 1) How much work does the gravitational force do on the ball from A to B? 2) What is the speed of the ball at point B? 3) What is the tension in the cord at point B? 4) What initial velocity...
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