1. PHYS 101 Learning Object
Energy of a Horizontal Mass-Spring System (Simple Harmonic Motion)
Below is a horizontal mass-spring system undergoing simple harmonic motion. Assuming that the
surface is frictionless, the total energy of this oscillating system will be the sum of the mass's
kinetic energy (K) and the spring's elastic potential energy (U).
The three bar charts shown below depict the ratio between kinetic energy (in red) and potential
energy (in blue) of the mass-spring system at a certain time during the oscillation. For each chart,
rationalize where the mass would be located (in terms of x) and the elasticity (e.g. stretched or
compressed) of the spring.
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x = Ax = 0x = -A
2. PHYS 101 Learning Object Answers
Energy of a Horizontal Mass-Spring System (Simple Harmonic Motion)
In this bar chart, kinetic energy represents the total energy of the mass-spring
system. Knowing that kinetic energy is possessed by an object due to its motion,
we can see that the mass must be located where x = 0 (equilibrium position) at
maximum speed since potential energy is absent from the chart. At x = 0, the
spring with neither be compressed nor stretched as it is midway from x = -A and
x = A.
Here, potential energy represents the total energy of the oscillating system. This
means that the mass must either be stationed furthest away from the wall at x = A
or closest to the wall at x = -A. At the farthest point, the spring is stretched out
completely and this work is fully stored as potential energy. When the spring is
compressed, this work is also fully stored as potential energy.
Unlike the two bar charts shown above, the total energy of the mass-spring system
is represented by both kinetic energy and potential energy, where K > U. Here, the
mass must have a nonzero speed that is less than its maximum speed since
potential energy is present. This means that the mass cannot be positioned at x =
A, x = 0, or x = -A, and instead, is located between these three points ( -A < x < 0 or
0 < x < A) where the spring can either be slightly stretched or slightly compressed.
