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    Mass and spring combination

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    A mass sits on a frictionless table. It is attached to a wall by a spring. The mass is initially located at x = 0 when the spring is unstretched (equilibrium position). You pull the mass away from the equilibrium position, out to x = A, and then release it. The mass then oscillates horizontally back and forth in simple harmonic motion.
    Which of the statements below are true about this motion?
    (Give ALL correct answers: B, AC, BCD .., or None)

    A) The speed of the mass is maximum at x = 0
    B) The total energy of the mass-spring system at x = A is the same as the total energy at x = 0
    C) Simple harmonic motion can also be referred to as periodic motion
    D) The potential energy of the mass-spring system is maximum at x = 0
    E) The magnitude of the acceleration of the mass is maximum at x = A

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    Solution Preview

    Please see the attached file.

    Correct answers: A, B, C and E.
    The motion of the mass can be described as: x = A cos (ωt).
    The velocity of the mass will be equal to dx/dt. Thus v = - Aω sin (ωt).
    When the mass is at x = 0 this means that cos (ωt) = 0 and the magnitude of sin (ωt) will thus be ...

    Solution Summary

    This solution looks at mass and spring properties when in simple harmonic motion. Several potential statements are analyzed.