HW 5 Solutions
Energy of Harmonic Oscillators
As you know, a common example of a
harmonic oscillator is a mass attached to a
spring. In this problem, we will consider a
moving block attached to a
spring. Note that, since the gravitational
potential energy is not changing in this case,
it can be excluded from the calculations.
For such a system, the potential energy is
stored in the spring and is given by
is the force constant of the spring and
is the distance from the equilibrium position.
The kinetic energy of the system is, as always,
is the mass of the block and
is the speed of the block.
We will also assume that there are no resistive forces; that is,
Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in
the figure . Assume that the force constant
, the mass of the block,
, and the amplitude of
, are given. Answer the following questions.
Which moment corresponds to the maximum potential energy of the system?
Note that the sign of
does not matter, just its magnitude, because
b) Which moment corresponds to the minimum kinetic energy of the system?