Harmonic Motion: The Spring Objective: The purpose of this experiment to study the simple harmonic motion of an object placed on the spring. Harmonic motion involves the principle of oscillation where the spring force is proportional to the spring? s elongation. This means that the further the spring was stretched, there was increase in the force in order to keep the spring extended. The experiment is divided into two parts. In the first part, I measured static equilibrium and in the second part, I measured the period of oscillation known as dynamic oscillation. Apparatus: The equipment was pole with a spring attached to top at its arm.
Metric ruler was attached to the pole, which was used to measure the extension of the spring from its initial position to its final position. On the bottom of the spring, there was a hook that was used as the index point where the measurement was made. Also, the hook was used for attachment of the hanger with the slotted weight. Theory: In static equilibrium, force of a spring is proportional to and directed opposite to the elongation. This is represented by Hooke? s Law where the restoring force is equal to elongation distance from equilibrium multiplied by the constant force of the body. From that equation, the experimenter will know how much force is needed to be applied to the spring in order to stretch it a particular distance.
The experiment also deals with dynamic oscillation that deals with the period of oscillation, which is independent of displacement. The period of oscillation is only depended on the effective mass and the spring constant. Procedure: 1. I weighted the spring and recorded its mass. 2.
I hanged the spring vertically from the arm of the pole. I used the bottom of the hook on the spring as the reference point where I would measure the length of elongation. I read the initial length of the spring to the nearest millimeter. 3.
Then I attached the hanger with a 10 gm slotted weight. I weighted the hanger to make sure that it is exactly 50 gm. Recorded the new position of the spring and the displacement X from the initial position of the spring. 4. I displaced the weight about 5 cm from the equilibrium and released it.
This made the hanger oscillate and I recorded the amount of time, it took for 20 complete oscillations to occur and determined the period from this. 5. Then I proceeded to take seven more measurements of displacement and the period where each time, 20 gm mass was added to the hanger and repeated the steps 2 and 3. The hanger? s weight increased with each measurement. 6. Plotted the applied weight (F) versus the displacement (X).
The slope of this graph was equal to the spring constant. 7. Then, I plotted another graph with the T squared versus the effective mass of the applied weight. The slope of this graph was supposed to be proportional to the spring constant. Questions: 1. If the spring is stretched too much it will deform and not return to its original shape.
This will affect the spring constant by that the force of the spring will no longer be proportional to the elongation because the spring will have a different initial position as the result of its deformation and loss of elasticity. 2. The displacement of oscillation must be kept small because the spring will not lose its elasticity and will be able to return to its original position.