A wall clock measures time using a vertical spring-mass system. The...

The time period of a vertical spring-mass system is given by $T = 2\pi \sqrt{\dfrac{m}{k}}$.

The time period depends only on the mass $m$ and the spring constant $k$, and is independent of the acceleration due to gravity $g$.

When the clock is transported from the equator to the poles, the value of $g$ increases, but the mass $m$ and the spring constant $k$ remain constant.

Since the time period $T$ does not depend on $g$, the clock will continue to operate with the exact same time period.

Therefore, the clock will give the correct time at the poles.