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Unformatted text preview: 1 Simple Harmonic Motion Learning Objectives: During this lab, you will 1. communicate scientific results in writing. 2. estimate the uncertainty in a quantity that is calculated from quantities that are uncertain. 3. learn how to use a histogram to analyze a data set. 4. fit a function more complicated than a straight line to a data set. 5. test a physical law experimentally. A. Introduction A body will oscillate in linear simple harmonic motion if it is acted upon by a restoring force whose magnitude is propor- tional to the linear displacement of the body from its equilibrium position ( F = - kx ). Similarly, a body will oscillate in rotational simple harmonic motion if there is a restoring torque that is proportional to the angular dis- placement of the body from its equilibrium position ( τ = - k θ ). For this experiment, you will explore both kinds of harmonic motion. You will use the most common exam- ple of linear simple harmonic motion, an object attached to a spring (see Fig. 1a). The most common example of rotational simple harmonic motion is the simple pendulum where, for small angular displacements of the pendulum from the equilibrium ( vertical ) position, the restoring torque is approximately proportional to the angle of displacement. We have chosen another example for this experiment, the torsion pendulum. A long cylindrical metal rod is held fixed in a support bracket with a heavy cylindrical plate attached to its lower end (Figure 1b). If you rotate the plate through an angle θ , the rod will exert on the plate a restoring torque that is proportional to θ , as long as θ does not exceed the elastic limit of the rod. If you rotate the plate and release it, the plate will oscillate in simple harmonic motion. From measurements of the period of the oscillation and the geometry of the rod and plate, you can calculate the torsion modulus, a quantity that characterizes the resistance of a material to twisting. You must write a report for this lab. B. Apparatus The two setups are a spring and a tor- sion pendulum. The spring apparatus includes hanging masses suspended from a spring attached to a ring stand. A sonic motion detector interfaced to a computer running LoggerPro determines the position of the hanging mass. The torsion pendulum is a metal rod, mounted in a wall bracket, with a metal plate and cylinder. You will also use a meter stick, calipers, computer and Logger Pro . Most of the pendula are constructed with aluminum plates, but a few use either grey- or blue-painted iron. The masses of each type of plate are in Table 1. SHM Simple Harmonic Motion revised July 11, 2005 Figure 1b Figure 1a m k s Figure 1: Schematics for experimental setups. a) Spring-mass (linear) oscillator....
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- Spring '08
- Simple Harmonic Motion