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 harmonicmotion.
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

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.

... we get two possible values of r, so the general solution to (1.9) is a linear combination of the ... The expert examines the mass attached to a vertical spring. ...

... are joined and connected to a block of mass 0.245 kg ... displaced by L then extension in each spring will be ... 2). Thus for the combination of the springs we can ...

... about the total momentum of the combination before the ... Compare the times during which the spring pushed on ...Mass (g) position released (cm) position caught (cm ...

... and the sum of the resulting spring reactions is fy2 ... results in torque from the horizontal springs equal t1 ... Therefore we assume that the mass hit an edge going ...

... A 50-kg rider on a moped of mass 75 kg ... s favorite exercise equipment at the gym consists of various springs. ... grip attached to the free end of a spring to 0.80 ...

... if fused together (then we get a single mass of 2m linked to two springs with spring constant k). Now, the motion of each mass is a linear combination of these ...

... And the length of spring of spring constant 4k is and thus ... to three different springs such that two springs are in ... potential energy of a particle of mass m, at ...

... The spring location in a control valve determines the ... on a series of assumptions, using mass and energy ... models that are a compromise combination of theory ...

... T = 149 N. 6. Time period of oscillations of a mass m resting on a spring of constant ... Let equivalent resistance of the left parallel combination be R1. ...