Chapter 17

Question 1

Displacement and amplitude definition

Answer 1

Displacement,x, is the distance from the equilibrium position

Amplitude, A, is the maximum displacement

Question 2

Period and frequency definition

Answer 2

Period, T, is the time taken for one complete oscillation
Frequency, Hz, is the number of complete oscillations per unit time

Question 3

Phase difference definition and angular frequency

Answer 3

Phase difference, φ, is the difference in displacement between two points on waves

Angular frequency, ω, the rate of change of angular position, given by 2𝜋f

Question 4

What is simple harmonic motion

Answer 4

Simple harmonic motion is a type of oscillation where the acceleration is directly proportional to the displacement

Given by 𝑎 = −𝜔²𝑥

Question 5

Why is acceleration negative

Answer 5

because acceleration is always in the opposite direction to displacement, towards the equilibrium

Question 6

An oscillator in simple harmonic oscillation is:

Answer 6

An isochronous oscillation, so the period is independent of amplitude

Question 7

How to determine the frequency/period of a SHM

Answer 7

Use a fiducial marker at the equilibrium position
Use a stopwatch to measure the time it takes for 10 periods to occur, then divide it by 10
This gives a period and the reciprocal is the frequency

Question 8

equation to determine the displacement of an oscillator

Answer 8

x = cos(𝜔t) or x = sin(𝜔t) depending on where the oscillator starts from

Question 9

velocity and acceleration

Answer 9

velocity at any point is determined by

𝑣 = ±𝜔sqrt(𝐴² − 𝑥²)

Question 10

Interchange between kinetic and potential energy

Answer 10

The kinetic energy + potential energy will be equal to the total energy at any point

Question 11

Damping

Answer 11

The process by which amplitude decreases over time by an external force acting on the system

Kinetic energy is converted to other forms, usually heat

Question 12

Types of damping

Answer 12

Light damping -
Amplitude decreases exponentially at a slow rate, which happens due to natural forces like friction or drag

Heavy damping - amplitude decreases dramatically, like when the oscillator is in water

Very heavy damping - oscillator doesn’t oscillate at all, like when it moves through oil

Question 13

free vs forced oscillations

Answer 13

free oscillations occur when a body oscillates without a driving force. In this case, it oscillates at its natural frequency

Forced oscillation - an external periodic driving force oscillates the body. The body will oscillate at the frequency of the driving force

Question 14

resonance

Answer 14

when the frequency of the external driving force matches the natural frequency, the amplitude of the oscillator significantly increases

Question 15

practical examples of resonance

Answer 15

Used in MRI machines to be able to scan inside the body without harmful methods like X-rays

Used in tuning circuits to amply the correct frequency from transmitters to reduce and make audio clearer against static noise

Question 16

Damping and resonance

Answer 16

The frequency at which maximum amplitude occurs decreases below the natural frequency, and the maximum amplitude itself decreases

Both decrease according to the severity of the damping