LABORATORY 4: BALLISTIC PENDULUM
Introduction In this experiment you will use the ballistic pendulum to study an inelastic collision. This device is a simplified version of equipment used to measure the muzzle velocity of a rifle. In the rifle experi
Problem : At what point during the oscillation of a spring is the force on the mass greatest?
Recall that F = - kx . Thus the force on the mass will be greatest when the displacement of
the block is maximum, or when x = x m .
Problem : What is the period
Simple Harmonic Motion
>From our concept of a simple harmonic oscillator we can derive
rules for the motion of such a system. We start with our basic force
formula, F = - kx . UsingNewton's Second Law, we can substitute for
force in terms of acceleration:
Energy of a Simple Harmonic Oscillator
Consider a simple harmonic oscillator completing one cycle. In the jargon of
conservative vs. nonconservative forces (see Conservation of Energy the
oscillator has completed a closed loop, and returns to its initial
Oscillating system - Any system that always experiences a force acting against the
displacement of the system (restoring force).
Restoring force - A force that always acts against the displacement of the system.
Periodic Motion - Any motion in which
The position of an object along a straight line can be uniquely identified by its
distance from a (user chosen) origin. (see Figure 2.1). Note: the position is fully
specified by 1 coordinate (that is why this a 1 dimensional problem).
2. MOTION IN A STRAIGHT LINE
In mechanics we are interested in trying to understand the motion of objects. In
this chapter, the motion of objects in 1 dimension will be discussed. Motion in
1 dimension is motion along a straight line.
The motion of a particle in one dimension is simple. Its velocity is either
positive or negative: positive velocity corresponds to a motion to the right
while negative velocity corresponds to a motion to the left. To describe the
The motion of objects in one-dimension are described using word, diagrams, numbers, graphs, and
Newton's three laws of motion are explained and their application to the analysis of the motion of objects in
We begin our study of oscillations by examining the general definition of an oscillating
system. From this definition we can examine the special case of harmonic oscillation, and
derive the motion of a harmonic system.
Definition of an Oscillating System
Variables of Oscillation
In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we
must introduce some new variables that describe the periodic nature of the motion:
amplitude, period, and frequency.
We have already studied the most common types of
motion: linear and rotational motion. We have developed the
concepts of work, energy, and momentum for these types of
motion. To complete our study of classical mechanics we must
finally examine the complic
An object in circular motion has an easily defined period, frequency and angular velocity.
Can circular motion be considered an oscillation?
Though circular motion has many similarities to oscillations, it can not truly be considered an
The maximum compression of an
oscillating mass on a spring is 1 m, and
during one full oscillation the spring
travels at an average velocity of 4 m/s.
What is the period of the oscillation?
Since we are given average velocity,
and we want to fin