2LC_Lab_1_HarmonicOsc7_3 - Physics 2LC Hookes Law and...

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Physics 2LC Hooke’s Law and Harmonic Oscillation (Pre lab assignment included) Objective: To experimentally study: Hooke’s Law of elasticity Simple Harmonic motion The static and dynamic description of elastic materials is rooted in two basic concepts: Hooke's Law and Simple Harmonic Oscillation. The elastic behavior of many materials can be described in terms of Hooke's Law , F = - kx . In words: “When an elastic material is stretched or compressed (displaced) from equilibrium by an amount x , the restoring force is proportional to the amount stretched or compressed (displacement).” When we have Hooke's Law, Simple Harmonic Oscillation can take place. A large spring will be used to verify Hooke's Law, and to measure oscillation periods in a simple harmonic oscillator. The Apparatus: 1. A 2-meter stick attached to a vertical support rod, mounted on the lab bench. Weight Meter Stick Photogate Plastic Plate Spring 2. A movable clamp with horizontal rod to support the spring and masses. 3. The spring. 4. A clear plastic plate with a black line, used to interrupt the PhotoGate for period measurements. 5. Weight Set consisting of: a) A 50 gram hanger b) Masses of 50 g, 100 g, and 200 g Masses between 50 and 400 grams can be selected, in 50 gram increments. 6. Photogate timer clamped to vertical support rod. 7. Pasco PasPort interface, Computer with Data Studio software for period measurements and data fitting. CAUTION: DO NOT OVER-STRETCH OR TWIST THE SPRING - IT WILL NOT RETURN TO ITS ORIGINAL LENGTH AND SHAPE.
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The Physics The basics of Hooke's Law and Simple Harmonic Oscillation are well covered in your text. Following is a brief summary. Physics - Hooke's Law = F restoring We will use a spring hanging vertically, stretched by weights connected to its lower end. If we neglect the mass of the spring, a free body diagram for the hanging mass gives F total = mg – kx = 0 in equilibrium. The displacement, x, is measured from the equilibrium position of the spring without added mass. In the lab, we will vary the mass m and measure the corresponding displacement x for each mass. Since mg = kx (1) a plot of mg versus x will have a slope of k , the spring constant. Physics - Simple Harmonic Oscillator A simple harmonic oscillator consisting of a massless spring with constant k , and a mass m will have a period of oscillation (time taken for one complete cycle) T given by: T = 2 π m k (2) If the spring is stiff (large k ), the period is less and vice versa. Similarly, a larger masses lead to a larger inertia and a longer T.
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2LC_Lab_1_HarmonicOsc7_3 - Physics 2LC Hookes Law and...

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