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2. An elastic string of m attached to it at a distance ' The other end...
An elastic string of negligible mass has one end fixed to a ceiling at point A....
An elastic string of negligible mass has one end fixed to a
ceiling at point A. The other end, point B, which is attached to a
particle of mass 3 kg, is in a position such that it is vertically
below point A, with the distance AB equal to 0.7 m. The mass is
released from rest. If the modulus of elasticity of the string is
35 N and its natural length is 1.3m find i) The distance of the...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cr...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
Pulley Problem
In the figure, a particle \(A\) of mass \(m\) is connected to another particle \(B\) of mass \(2 m\) by an inextensible string which passes over a smooth fixed pulley. A third particle \(C\) of mass \(m\) is connected to \(A\) by an elastic string of natural length \(L\). All the particles are initially held with the elastic string just unstretched and are then released from rest. You can assume that the tension of the elastic string is directly proportional...
One end of a 1.20-m string is held fixed. The other end is attached to a...
One end of a 1.20-m string is held fixed. The other
end is attached to a weightless ring that can slide along the
frictionless rod as shown in the diagram.
a.) What are the three longest possible wavelengths
for standing waves on this string (in meters, based on L=1.20)?
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs,...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
Consider an elastic string of length L whose ends are held fixed. The string is set in motion fro...
Answer needed in form summation from n=1 to infinity:
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
Consider an elastic string of length L whose ends are held fixed. The string is set...
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity wx,0) - parts (b) and (c). (A computer algebra system is recommended.) x). Let L = 18 and 2 = 1 in g(x) = (a) Find the displacement u(x, t) for the given [x). (Use a to represent an arbitrary constant.) Ux. 1) - ECO , (h) Plot uix, t) versus x for OS...
One end of a 0.80 m string is fixed, the other end is attached to a...
One end of a 0.80 m string is fixed, the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the bottom point at 10 m/s. What is the radial acceleration of the stone at the top of the circle? (Ans: 86 m/s2)
Question 2 A particle of mass m, is attached to a spring of natural length 2le...
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
2. A small box of mass m is kept on a fixed, smooth sphere of radius...
2. A small box of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the box makes an angle of 30° with the vertical. The box is released from the position. (a) What is the force exerted by the sphere on the box just after the release? (b) Find the distance travelled by the box before it leaves contact with the sphere. 3. A particle is suspended from a fixed...
An elastic string of negligible mass has one end fixed to a
ceiling at point A. The other end, point B, which is attached to a
particle of mass 3 kg, is in a position such that it is vertically
below point A, with the distance AB equal to 0.7 m. The mass is
released from rest. If the modulus of elasticity of the string is
35 N and its natural length is 1.3m find i) The distance of the...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
One end of a 1.20-m string is held fixed. The other
end is attached to a weightless ring that can slide along the
frictionless rod as shown in the diagram.
a.) What are the three longest possible wavelengths
for standing waves on this string (in meters, based on L=1.20)?
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
Answer needed in form summation from n=1 to infinity:
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity wx,0) - parts (b) and (c). (A computer algebra system is recommended.) x). Let L = 18 and 2 = 1 in g(x) = (a) Find the displacement u(x, t) for the given [x). (Use a to represent an arbitrary constant.) Ux. 1) - ECO , (h) Plot uix, t) versus x for OS...
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
2. A small box of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the box makes an angle of 30° with the vertical. The box is released from the position. (a) What is the force exerted by the sphere on the box just after the release? (b) Find the distance travelled by the box before it leaves contact with the sphere. 3. A particle is suspended from a fixed...
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