# Mass and spring combination

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

https://brainmass.com/physics/periodic-motion/mass-and-spring-combination-5548

#### 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.