"A meter stick is held vertically behind an object on a spring. The object vibrates from the 20cm mark to the 32cm mark on the stick. Find the displacement when the object is at the 20cm mark, 24cm mark, 26cm mark, and 30cm mark."
I had found the equilibrium position to be 26cm, and the amplitude to the 6cm. However, when they ask for displacement, do they mean in reference to the equilibrium position, or where the object begins moving (20cm)?
When they ask for the displacement at different positions, they are usually referring to the displacement in reference to the equilibrium position. In this case, the equilibrium position is at 26cm on the meter stick.
To calculate the displacement at different positions, subtract the position of the object from the equilibrium position (26cm) at each given point:
1. Displacement at 20cm mark:
20cm - 26cm = -6cm
The displacement at the 20cm mark is -6cm, meaning the object is 6cm to the left of the equilibrium position.
2. Displacement at 24cm mark:
24cm - 26cm = -2cm
The displacement at the 24cm mark is -2cm, indicating that the object is 2cm to the left of the equilibrium position.
3. Displacement at 26cm mark:
26cm - 26cm = 0cm
The displacement at the 26cm mark is 0cm, meaning the object is at the equilibrium position itself.
4. Displacement at 30cm mark:
30cm - 26cm = 4cm
The displacement at the 30cm mark is 4cm, indicating that the object is 4cm to the right of the equilibrium position.
Remember, displacement is the distance and direction from the equilibrium position.