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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 (&#969;t).
The velocity of the mass will be equal to dx/dt. Thus v = - A&#969; sin (&#969;t).
When the mass is at x = 0 this means that cos (&#969;t) = 0 and the magnitude of sin (&#969;t) will thus be ...

#### Solution Summary

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

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