Question

Is the potential energy of a spring always positive

Answer 1

P.E=1/2kx°2

P.E depends on the amplitude of the body.
Amplitude of the body can be positive or negative in a sinusoidal wave so P.E of the body can also be positive or negative.

Answer 2

potential energy can be negative only when when force of gravity ( g ) acts in opposite direction of the motion. so, potential energy is always positive for a spring.