IB Physics Mass and Spring

/

A tutorial sheet of questions on a mass and a spring is given below.

  1. Two springs each of force constant k are connected in series and held vertically. A mass M is placed on the lower end of the combination. What is the extension produced?
  2. A mass M rests on a smooth horizontal surface. Identical springs of force constant k are attached to opposite sides of the mass. The other ends of the springs are held at rest. What is the period of oscillation of the mass when it is released after being displaced (a) along the line of the springs, (b) perpendicular to the line of the springs.
  3. A spring of force constant k is held vertically with its upper end fixed. A mass M is placed on the lower end of the spring. The mass is then pulled down a distance A and released from rest. (a) Explain why the period of oscillation does not depend on g. (b) Does the period of oscillation does depend on A? (c) Instead of being released from rest the mass is given an initial velocity u downwards at the pulled down position. What is the period of the oscillation in this case?
  4. Does a mass oscillating on a spring in a vertical plane have gravitational potential energy?
  5. A light spring is hanging loosely from the ceiling. A mass is placed on the free end of the spring and released from rest. The mass moves downwards a distance of 40 cm before starting to rise again. What is the period of the simple harmonic motion?[0.90s]
  6. A block of mass M is connected to a light spring of force constant k. The block is placed on a smooth inclined plane of angle of elevation 𝜽. The other end of the spring is held at rest with the spring parallel to the inclined plane. The mass is set moving in simple harmonic motion. Does the period of oscillation depend on 𝜽?
  7. A block of mass M slides a distance d from rest down a smooth inclined plane making an angle 𝜽 with the horizontal. It hits a light spring of natural length L and force constant k at the bottom of the incline. Determine the amount that the spring is compressed when the block comes to rest.
  8. A bungee jumper of mass M is attached to an elastic cord of unstretched length L and force constant k. If they jump from rest how far do they fall before they come to rest?