# A-level Physics (Advancing Physics)/Energy in Simple Harmonic Motion/Worked Solutions

**1. A 10g mass causes a spring to extend 5cm. How much energy is stored by the spring?**

Gravitational Potential Energy transferred completely to Elastic Potential Energy

Gravitational Potential Energy = mass x gravity x height

GPE

**2. A 500g mass on a spring (k=100) is extended by 0.2m, and begins to oscillate in an otherwise empty universe. What is the maximum velocity which it reaches?**

**3. Another 500g mass on another spring in another otherwise empty universe is extended by 0.5m, and begins to oscillate. If it reaches a maximum velocity of 15ms ^{-1}, what is the spring constant of the spring?**

**4. Draw graphs of the kinetic and elastic energies of a mass on a spring (ignoring gravity).**

**5. Use the trigonometric formulae for x and v to derive an equation for the total energy stored by an oscillating mass on a spring, ignoring gravity and air resistance, which is constant with respect to time.**

Substitute these into the equation for the total energy:

We know that:

Therefore:

By substitution: