Calculate Spring Constants: 0.400 and 0.225 Joules

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To calculate the potential energy stored in a spring, use the formula PE = 0.5 * k * x², where k is the spring constant and x is the displacement from equilibrium. For a spring with a force constant of 500.0 N/m, when stretched 4.00 cm (0.04 m), the potential energy is 0.400 Joules. Similarly, when the spring is compressed 3.00 cm (0.03 m), the potential energy is 0.225 Joules. This demonstrates the relationship between displacement and stored energy in springs. Understanding this formula is essential for solving spring energy problems effectively.
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Can someone please just explain to me how to do this? I feel helpless.

A spring has a force of 500.0 N/m. Show that the potential energy stored in the spring is as follows:

a.) 0.400 Joules when the spring is stretched 4.00cm from equilibrium.
b.) 0.225 Joules when the spring is compressed 3.00cm from equilibrium.
 
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You should know the formula for a spring's potential 'stored' energy. Or you can derive if from the fact that the work done in dispacing a spring from its equilibrium oposition to a distance X is equal to the negative of its potential energy change.
 

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