Option 1: If the motion of an oscillating liquid column in a U-tube is periodic but not simple harmonic, it means that the oscillations repeat over a fixed time interval but do not follow the characteristics of simple harmonic motion. Simple harmonic motion is defined by a restoring force that is directly proportional to the displacement from the equilibrium position. If the oscillating liquid column doesn`t meet this criteria, option 1 is not applicable.

Option 2: If the motion is non-periodic, it means that the oscillations do not repeat in a regular manner. Non-periodic motion can be unpredictable and irregular, and it does not have a defined time period. Therefore, option 2 is also not applicable for the motion of an oscillating liquid column in a U-tube.

Option 3: If the motion is simple harmonic and the time period is independent of the density of the liquid, it means that the liquid column oscillates with a constant time period regardless of the liquid`s density. This does not accurately describe the motion of an oscillating liquid column in a U-tube as the time period can vary depending on the density of the liquid.

Option 4: The correct answer is option 4. If the motion is simple harmonic and the time period depends