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So my teacher handed out a practice test in preperation for our test tomorrow, and I understand a majority of the problems, but need help with a few problems. Any help would be greatly appreciated.

1. A mass m is attached to a light string of length R, and the other end of the string is attached to a fixed point above, making a pendulum. The mass is pulled out to the side so the string makes an angle (theta) with the vertical

http://img141.imageshack.us/img141/232/circleqq9.jpg [Broken]

a. If the mass is released in this position, what is the tension in the string immediately after the release? (I got that T=mgcos(theta). )

b. If the mass is released in this position, what is the tension in the string at the moment when the mass passes through the bottom of the swing? (No idea)

c. Instead of being released from rest, the mass is given an initial speed tangent to the circle downwards (SE in the diagram). Find the minimum value of v so that the mass travels in a complete vertical circle of radius R (No idea whatsoever)

2.A special spring is constructed in which the restoring force is in the opposite direction to the displacement, but is proportional to the cube of the displacement; ie, F=-kx^3

This spring is placed on a horizontal frictionless surface. One end of the spring is fixed, and the other end is fastened to a mass M. The mass is moved so that the spring is stretched a distance A and then released. Determine each of the following in terms of k, A, and M.

a. The potential energy in the spring at the instant the mass is released. (U=((KA^4)/4)

b.The maximum speed of the mass (square root ((KA^4)/2M))

c. The displacement of the mass at the point where the potential energy of the spring and the kinetic energy of the mass are equal (Once again, no idea)

3. I've got this problem down and don't need any help, although I'll post it if anyone's interested.

Again, thanks for any help at all.

1. A mass m is attached to a light string of length R, and the other end of the string is attached to a fixed point above, making a pendulum. The mass is pulled out to the side so the string makes an angle (theta) with the vertical

http://img141.imageshack.us/img141/232/circleqq9.jpg [Broken]

a. If the mass is released in this position, what is the tension in the string immediately after the release? (I got that T=mgcos(theta). )

b. If the mass is released in this position, what is the tension in the string at the moment when the mass passes through the bottom of the swing? (No idea)

c. Instead of being released from rest, the mass is given an initial speed tangent to the circle downwards (SE in the diagram). Find the minimum value of v so that the mass travels in a complete vertical circle of radius R (No idea whatsoever)

2.A special spring is constructed in which the restoring force is in the opposite direction to the displacement, but is proportional to the cube of the displacement; ie, F=-kx^3

This spring is placed on a horizontal frictionless surface. One end of the spring is fixed, and the other end is fastened to a mass M. The mass is moved so that the spring is stretched a distance A and then released. Determine each of the following in terms of k, A, and M.

a. The potential energy in the spring at the instant the mass is released. (U=((KA^4)/4)

b.The maximum speed of the mass (square root ((KA^4)/2M))

c. The displacement of the mass at the point where the potential energy of the spring and the kinetic energy of the mass are equal (Once again, no idea)

3. I've got this problem down and don't need any help, although I'll post it if anyone's interested.

Again, thanks for any help at all.

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