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

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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).


Simple HArmonic Motion


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: