When the displacement of a mass on a spring is one half of the amplitude of its oscillation,what fraction of the total energy is kinetic energy?
A)¼
B)½
C)¾
D)⅓
E)⅔

Question

Quizplus · Accepted Answer

The total energy of an oscillating mass on a spring is given by the equation:
Total energy = ½ kA^2
where k is the spring constant and A is the amplitude of oscillation.
When the displacement of the mass is one half of the amplitude, its displacement is A/2.
The total energy of the system at this displacement is:
Total energy = ½ k(A/2)^2
Total energy = ½ kA^2/4
Total energy = ¼ (½ kA^2)
Since the kinetic energy equals half of the total energy at any point in the motion, we can conclude that:
Kinetic energy = ¼ (½ kA^2) / 2
Kinetic energy = ¼ (½ kA^2) / 2
Kinetic energy = ¼ (¼ kA^2)
Kinetic energy = ¼ of the total energy.
Thus, the fraction of the total energy that is kinetic energy at this displacement is ¾ or choice C.

When the Displacement of a Mass on a Spring Is