please show all work

In space astronauts can't stand on a scale to be weighed. To determine their mass, they sit in a chair attached to a spring, which has a spring constant of 750N/m. The chair has a mass of 20.0kg Caleb sits in the chair and Jordan pushes him 15.0cm to the left and holds him at rest 40.0cm from the wall with force F. When released at rest, Caleb (and the chair) vibrate back and forth. Caleb is found to go thru exactly 5 cycles in 12.0 seconds. The ship is far from Earth and all other planets. Caleb's position when no force is applied to him: spaceship wall 15.0cm Caleb's position when a force F holds him at rest in the starting position. x=40.0cm a) Find the force F needed to hold Caleb at rest. b) What is the name for this kind of motion? c) Find Caleb's mass. Start with equations from the formula sheet; show the equation in symbolic form then show all work to apply that equation. d) Find Caleb's maximum speed in m/s when he is in the chair. e) At what distance x from the wall does the maximum speed occur