Oscillations

1. Verify that a solution to Newton's Second Law is a sinusoid.

2. Derive, from the concept of the total energy of a system, the total energy of an oscillating system in terms of k and amplitude.

3. A block with mass m rests on a frictionjless surfae and is connected to a horizontal spring of force constant k. The other end of the spring is attahced to a wall. A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is given. Find the maximum amplitude of the oscialltion such that the top block will not slip on the bottom block.

4. A block is on a piston which is moving vertically with a simple harmonic motion of period 1.0 sec. At what amplitude of motion will the block and piston separate? If the piston has an amplitude of 5.0 cm, what is the maximum frequency for which the block and piston will be in contact continously?

5. Two springs are joined and connected to a mass m such that they are all in a straight line. The two springs are connected first and then the mass last so that all three are in a row. If the springs have a stiffness of k