Question

A system consisting of a mass of one gram fixed to a spring which is stretched by 1 cm. by a force of 10000 dynes, the particle being constrained to move only along the x axis. What will be the zero-point energy?

Answer 1

By conservation of energy, the zero-point energy will be

$$E_0=\dfrac 12kx^2=\dfrac12\dfrac{F}{x}x^2=\dfrac 12Fx=500\space\mu\text{J}.$$