Need Help with this Physics Problem?

Question

At t = 0, a 715 g mass at rest on the end of a horizontal spring (k = 127 N/m) is struck by a hammer, which gives it an initial speed of 2.77 m/s.
1. Determine the period of the motion in seconds.
Determine the frequency of the motion.

2. Determine the amplitude.

3. Determine the maximum acceleration.

4. Determine the position as a function of time.
( ____ m ) sin[ ( _____ rad/s)t ]

5. Determine the total energy.

Any help regarding any of these numbers will be greatly appreciated. Please show all work. First person to get all answered correctly gets best answer. Thank you =).

Answer 1

The energy of the system is initially all kinetic:

E = 1/2 m v²

When the spring is extended and the mass stops for a split second, the energy is all potential:

E = 1/2 k A²

The period of the system is

T = 2π sqrt ( m / k )

For (1), you have the equation for period. For (2), set the kinetic and potential energies equal and solve for A. For (3) realize that the maximum acceleration occurs when the mass is fully extended and F = ma = kA. For (4) plug in the amplitude and the period. For (5), use either energy equation to compute the total energy.