Physics218Assign1 - ASSIGNMENT 1 Physics 218 Reading: Pain...

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ASSIGNMENT 1 Physics 218 Due Feb. 2 Spring 2008 Reading: Pain Ch 1-4. 1. Consider the following complex solution to a simple harmonic oscillator problem for a pen- dulum, z ( t ) = 12 cm exp[ i (12 π/st + 3)] exp[ - (0 . 25 /s ) t ], where cm and s are centimeters and seconds, respectively, and t is time. (a) Based on the equation, is this pendulum damped? Driven? Justify your answer. (b) Draw by hand a graph of x ( t ) vs t for 0 < t < 5 s . (c) Which of the list of variables r, s, ω, ω 0 , ˆ ω, γ, F 0 , α and φ can you extract from the equation above, and what are their values? Include units. (d) What is the period of oscillation of the pendulum (in seconds)? Is there any other characteristic time in the problem? 2. Show that one can ignore gravity when one studies the harmonic motion of a mass hanging on a spring. To answer the question, consider a mass m hanging on a spring with negligible mass and spring constant k . Let the length of the spring without the mass be ` 0 and the length of the spring with the mass hanging on it at rest be ` . Let y ( t ) be the displacement of the end of the spring from the equilibrium position when the mass is oscillating. m o l l (a) Draw a free body diagram of the mass, including the spring force and the force of gravity on the mass. (b) Utilize this diagram to determine the length of the spring
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Physics218Assign1 - ASSIGNMENT 1 Physics 218 Reading: Pain...

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