Category: Oscillations

A person swinging in a swing without anyone pushing it is an example of free oscillation. However, if someone pushes the swing periodically, the swing has forced, or driven, oscillations. Two angular frequencies are associated with a system undergoing driven oscillations: (1) the natural angular frequency ω of the system, which is the angular frequency at which it would oscillate if it were suddenly disturbed…

A pendulum will swing only briefly underwater, because the water exerts on the pendulum a drag force that quickly eliminates the motion. A pendulum swinging in air does better, but still the motion dies out eventually, because the air exerts a drag force on the pendulum (and friction acts at its support point), transferring energy from…

In 1610, Galileo, using his newly constructed telescope, discovered the four principal moons of Jupiter. Over weeks of observation, each moon seemed to him to be moving back and forth relative to the planet in what today we would call simple harmonic motion; the disk of the planet was the midpoint of the motion. The…

We turn now to a class of simple harmonic oscillators in which the springiness is associated with the gravitational force rather than with the elastic properties of a twisted wire or a compressed or stretched spring. The Simple Pendulum If you hang an apple at the end of a long thread fixed at its upper…

Figure 15-7 shows an angular version of a simple harmonic oscillator; the element of springiness or elasticity is associated with the twisting of a suspension wire rather than the extension and compression of a spring as we previously had. The device is called a torsion pendulum, with torsion referring to the twisting. Fig. 15-7   A torsion pendulum is an angular version of…

In Lesson 8 we saw that the energy of a linear oscillator transfers back and forth between kinetic energy and potential energy, while the sum of the two—the mechanical energy E of the oscillator—remains constant. We now consider this situation quantitatively. The potential energy of a linear oscillator like that of Fig. 15-5 is associated entirely with the spring. Its value…

Once we know how the acceleration of a particle varies with time, we can use Newton’s second law to learn what force must act on the particle to give it that acceleration. If we combine Newton’s second law and Eq. 15-8, we find, for simple harmonic motion, This result—a restoring force that is proportional to the…

Figure 15-1a shows a sequence of “snapshots” of a simple oscillating system, a particle moving repeatedly back and forth about the origin of an x axis. In this section we simply describe the motion. Later, we shall discuss how to attain such motion. One important property of oscillatory motion is its frequency, or number of oscillations that are completed each…

The springboard used in modern diving competitions is a complex mechanical system that a skilled diver must master. In a running dive, for example, a skilled diver knows how to first take three quick steps along the board to start the board oscillating and then leap to the free end of the board so as…