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Review E

# Review E - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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E-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2005 Review E: Simple Harmonic Motion and Mechanical Energy This Worked Example demonstrates the basics of Simple Harmonic Motion (SHO) and so is included as a review unit. An object of mass 2 4.0 10 kg m = × sitting on a frictionless surface is attached to one end of a spring. The other end of the spring is attached to a wall. Assume that the object is constrained to move horizontally along one dimension. The spring has spring constant 2 2.0 10 N/ m k = × . The spring is initially stretched a distance 2.0cm from the equilibrium position and released at rest. a) What is the position of the mass as a function of time? b) What is the velocity of the mass as a function of time? c) What is the time that it takes the mass-spring system to first return to its original configuration? d) How do the initial conditions for the position and velocity of the mass-spring system enter into the solution? e) What is the kinetic energy of the mass as a function of time? f) What is the potential energy of the spring-mass system as a function of time? g) What is mechanical energy of the spring-mass system as a function of time? Solutions: a) Choose the origin at the equilibrium position. Choose the positive x -direction to the right. Define ( ) x t to be the position of the mass with respect to the equilibrium position.

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Review E - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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