Chapter 15: "Periodic Motion"

Question 1

The frequency f of periodic motion is and is defined as:

Answer 1

Question 2

The SI unit of frequncy is:

Answer 2

Question 3

Simple harmonic motion

Answer 3

periodic motion in which the displacement of a system from its equilibrium position varies sinusoidally with time. A system moving in this way is called a simple harmonic oscilator.

Question 4

A restoring force that is linearly prorportional to displacement tends to…

Answer 4

A restoring force that is linearly prorportional to displacement tends to return a simple harmonic oscilator to it’s equilibrium postition

Question 5

For small displacements, restoring forces are generally…

Answer 5

generally prorportional to the displacement and therefore cause objects to execute simple harmonic motion about any stable equilibrium position

Question 6

What is a Phasor?

Answer 6

A rotating arrow whose component on a vertical axis traces out simple harmonic motion

Question 7

What is a “Reference Circle?”

Answer 7

The circle traced out by the tip of the phasor, and the length of the phasor is equal to the amplitude A of the simple harmonic motion

Question 8

Angular Frequency ω

Answer 8

Question 9

For a simple harmonic oscillator of amplitude A, the displacement x as a function of time is

Answer 9

Question 10

The arguement is the phase Φ(t) of the periodic motion

Answer 10

Question 11

The x components of velocity and acceleration of a simple harmonic scillator are

Answer 11

Question 12

Simple harmonic oscillator equation:

Answer 12

Question 13

The mechanical energy E of an object of mass m undergoing simple harmonic motion is:

Answer 13

Question 14

Fourier’s Theorem

Answer 14

Any periodic function with period T can be written a a sum of sinusoidal simple harmonic functions pf frequency f_n = n/T, where n is an integer. The n = 1 term is the fundamental frequency of the first harmonic, and the other components are higher harmonics.

Question 15

For an object attatched to a light spring of spring constant k, the simple harmonic oscillator takes the form

Answer 15

Question 16

For an object attatched to a light spring of spring constant k, the angular frequency of the oscillation is

Answer 16

Question 17

For an object attatched to a light spring of spring constant k, the motion of the object is described by

Answer 17

Question 18

If a torsional oscillator of rotational inertia I is twisted through a small angle from its equilibrium position ϑ₀ to position ϑ, the restoring torque τ_ϑ is

Answer 18

Question 19

When ϑ₀ = 0, the simple harmonic equation for the torsional oscillator is

Answer 19

Question 20

The rotational position ϑ of the torsional oscillator at instant t is given by

Answer 20

Question 21

For a torsiona oscillator, ω is

Answer 21

Question 22

For small rotational displacements, the simple harmonic oscillator equation of a pendulum is

Answer 22

Question 23

For small rotational displacements, the angular frequency of a pendulum is

Answer 23

Question 24

The period of a simple pendulum is

Answer 24

Question 25

torsional oscillator

Answer 25

A horozontal disk suspended at its center by a thin fiber

Question 26

A pendulum

Answer 26

Any object that swings about a pivot. A simple pendulum consists of a small object (the bob) attatched to a very ligh wire or rod.

Question 27

Damped Oscillation

Answer 27

The amplitude of SHM ecreases over time due to energy dissipation. The cause of dissipation is a damping forc due to friction, air drag, or water drag.

Question 28

Quality factor (Q) of a damped oscillator

Answer 28

A dampd oscillator had a quality factor Q that keeps oscillating for many periods.

Question 29

At low speeds, the damping force F^d_ao tends to be prorportional to the velocity of the object

Answer 29

Question 30

For small damping, the position x(t) of a damped spring is

Answer 30

Question 31

For small damping, the angular frequency of a spring ω_d is

Answer 31

Question 32

The time constant τ for a damped system is τ = m/b.The energy of a damped harmonic oscilator is reduced by a factor of 1/e.

The amplitude x_max(t) andenergy E(t) of a damped oscilation of initial amplitude A and initial energy E₀ decrease exponentially with time.

Answer 32

Question 33

Any object that undergoes simple harmonic motion obeys the simple harmonic oscilator equation:

Answer 33

Question 34

The quality factor Q of a system is

Answer 34