# Oscillations

## REVIEW & SUMMARY OSCILLATIONS

REVIEW &  SUMMARY OSCILLATIONS Frequency The frequenry f of periodic or oscillatory motion is the number of oscillations per second. In the SI system, it is measured in hertz I hertz = I Hz = I oscillation per second = I s -I Period The period T is the time required for one complete oscillation or cycle It is related …

## Damped Simple Harmonic Motion

Damped Simple Harmonic Motion A pendulum will swing only briefly under water, because the water exerts a pral force on the pendulum that quickly eliminates the motion. A pendulum winging iI air does better, but still the motion dies out eventually, because the air ‘exerts a dral force on the pendulum (and friction acts at its support) transferring …

## Simple Harmonic Motion and Uniform Circular Motion

Simple Harmonic Motion and Uniform Circular Motion In  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 …

## Measuring. g

Measuring. g We can use a physical pendulum to measure the free-fall acceleration g at a panicular location on Earth’s surface. (Countless thousands of such  easurements have been made during geophysical prospecting.) To analyze a simple case, take the pendulum to be a uniform rod of length L suspended from one end. For such a pendulum, h in the …

## The Physical Pendulum

The Physical Pendulum .A real pendulum, usually called a physical pendulum, can have a complican distribution of mass, much different from that of a simple pendulum. Does a physic pendulum also undergo SHM If sowhat is its period  shows an arbil!’VY physical pendulum displaced to one side I angle 8. The gravitational force 1,acts at its center of mass …

## The Simple Pendulum

The Simple Pendulum If you hang an apple at the end of a long thread fixed at its upper end. and then set the apple swinging back and forth a small distance, you easily see that the apple’s motion is periodic. Is it. in fact. simple harmonic motion If so what is the period T  To answer we …

## Pendulums

Pendulums We turn now to a class of simple harmonic oscillators in which the springiness is associated with the gra\’itational force rather than with the elastic properties of a twisted wire or a compressed or stretched spring.

## An Angular Simple Harmonic Oscillator

An Angular Simple Harmonic Oscillator shows an angular version of a simple harmonic oscillator; the element of  springiness or elasticity is associated with the twisting of a suspension wire  than the extension and compression of a spring as we previously had. The devic called a torsion pendulum, with torsion referring to the twisting. If we rotate the …

## Energy in Simple Harmonic Motion

Energy in Simple Harmonic Motion In Chapter 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 osciIIator-remains constant. We now consider this situation quantitatively. The potential energy of a linear osciIIator like that of Fig. 16-5 is …

## Sample Problem

Sample Problem This maximum speed occurs when the oscillating block is rushing through the origin; compare Figs. 16-4a and 16-4b, where you can see that the speed is a maximum whenever x = O. Sample Problem 16-1 A block whose mass m is 680 g is fastened to a spring whose spring constant k is …