Consider the 2017 exam questions..

To solve an oscillating spring problem you need....

• • the spring constant or data to determine the spring constant

  • the size of the mass that is oscillating

  • an understanding of the conservation of energy in the system

This doesn't seem like much information!

Let's consider the equations at play, this is an energy problem.

Total energy will be the combination of gravitational potential, kinetic and elastic potential.

Assumption: energy loss to environment is insignificant

Step 1. Set up the Energy equation:

Consider the motion of the mass. It oscillates so it will have a maximum and minimum height. Identify the variables. Watch your video of the oscillation.

The height gained from its lowest point will be used to measure its gravitational potential and the extension of the spring will be used to measure its strain potential, at both of these points the mass is at rest. Midway through its oscillation, the speed is at a maximum, thus kinetic energy is at a max.

Step 2.

Before release: Total energy =

At bottom of motion (maximum extension) Total energy =

Step 3.

The height gained is equivalent to the maximum extension so the above equations can be combined and solve for x