To calculate the maximum potential energy of a vertically loaded spring with an extension before it was set into oscillation with an amplitude, you need to consider both the extension and the amplitude. The potential energy stored in a spring is given by the formula:
PE = (1/2) * k * x^2
Where: PE is the potential energy stored in the spring, k is the spring constant, and x is the displacement or extension of the spring from its equilibrium position.
When the spring is set into oscillation, it oscillates between its maximum compression and maximum extension. The amplitude, A, represents the maximum displacement from the equilibrium position. In this case, we need to determine the maximum extension of the spring.
The maximum extension of the spring, xmax, can be calculated using the formula:
xmax = A + x
Where: xmax is the maximum extension, A is the amplitude, and x is the initial extension of the spring.
Once you have determined the maximum extension, you can calculate the maximum potential energy by substituting the value of xmax into the potential energy formula:
PE = (1/2) * k * xmax^2
Remember to consider both the initial extension, x, and the amplitude, A, when calculating the maximum potential energy of the vertically loaded spring.