tutorial_harmonic_motion

# tutorial_harmonic_motion - Simple harmonic motion SIMPLE...

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©2008 Physics Department, Grand Valley State University, Allendale, MI. 1 I. Differential equation of motion A block is connected to a spring, one end of which is attached to a wall. (Neglect the mass of the spring, and assume the surface is frictionless.) The block is moved 0.5 m to the right of equilibrium and released from rest at instant 1. The strobe diagram at right shows the subsequent motion of the block ( i.e., the block is shown at equal time intervals). A. Using Newton’s second law in one dimension, x m F net , write down the differential equation that governs the motion of the block. The net force exerted on the block may be called a restoring force. Justify this term on the basis of your differential equation above. B. Show by direct substitution that the functions x(t) given below are solutions to the differential equation you wrote down in part A. As part of your answer, specify the conditions (if any) that must be met by the parameters A, , and o in order for each function to be a valid solution. x(t) = A cos ( t + o ) x(t) = A sin ( t + o ) SIMPLE HARMONIC MOTION 0.5 m Equilibrium position 1 2 3 4 5 6 7 8 9 Block released from rest here

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Simple harmonic motion ©2008 Physics Department, Grand Valley State University, Allendale, MI. 2 C. Shown at right is the x vs. t graph representing the motion of the block described on the preceding page. Note that t = 0 corresponds to the instant (“instant 1”) when the block is released from rest. Suppose that the experiment described in section I were repeated exactly as before, except with one change to the setup. For each change described below, sketch the new x vs. t graph for the block. Show as much detail as possible in your new graph. Use your results from part B (on the preceding page) to justify your answers.
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## tutorial_harmonic_motion - Simple harmonic motion SIMPLE...

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