18 Simple Harmonic Motion

Question 1

Time period

Answer 1

Oscillating motion is the time for one complete cycle of oscillation

Question 2

Frequency

Answer 2

Oscillations in the number of cycles per seconds made by oscillating object

Question 3

Ψ

Angular frequency

Answer 3

2π / t

Question 4

Displacement

Answer 4

Of an object from equilibrium continually changes during the motion

Question 5

Phase difference

Answer 5

2πΔt / T

( in radians)
The time between successive instants when the two objects are at maximum displacement in the same direction

Question 6

Variation of velocity with time

Answer 6

Magnitude of the velocity is greatest when the gradient of the displacement-time graph is greatest

Velocity is zero when the displacement-time graph is zero

Question 7

Variation of acceleration with time

Answer 7

(Given by the gradient of the velocity-time graph)

Acceleration is greatest when the gradient of velocity-time graph is greatest, this is when the velocity is zero and maximum displacement

Acceleration is zero when the gradient of the velocity-time graph is zero. ( displacement is zero and velocity at maximum)

Question 8

Acceleration is always in the opposite direction to the displacement

True or false?

Answer 8

True

Question 9

Simple harmonic motion (conditions)

Answer 9

Proportional to displacement

Opposite direction to the displacement

a = -x

Question 10

Acceleration

Answer 10

a = -ω^2 x

Question 11

State two quantities that increase when the temperature of a given mass of gas is increased at a constant volume

Answer 11

Pressure and kinetic energy

Question 12

What assumptions are made when using the equation Q=ml

Answer 12

No heat is loss to the surrounding

100% efficient

Question 13

Simple harmonic motion

Answer 13

Acceleration is proportional to displacement

Direction is opposite to displacement

Question 14

Why is the motion is no longer simple harmonic motion

Answer 14

Bungee cord becomes slack
Motion under gravity
Constant acceleration

Question 15

Where on the bungee cord is the stress at a maximum

Answer 15

Stress = F/A

Force at this point includes the whole cord

Question 16

Larger amplitude ( pendulum)

Answer 16

Reduces air resistance

Question 17

Longer time period ( pendulum)

Answer 17

Reduces uncertainty in reaction time

Question 18

Uniform circular motion

Answer 18

When an object rotates at a steady rate / speed

Question 19

Angular speed

Answer 19

Angle displacement per second

Question 20

Angular displacement

Answer 20

Angle turned through in a time

Question 21

Centripetal acceleration

Answer 21

Acceleration of an object in uniform circular motion

Question 22

Free oscillation

Answer 22

A freely oscillating object oscillates with a constant amplitude

No frictional forces

Question 23

Damping

Answer 23

Damping occurs when frictional forces cause the amplitude of an oscillation to decrease

Question 24

Light damping

Answer 24

In this case the amplitude gradually decreases with time

Question 25

Critical damping

Answer 25

In this case the system returns to equilibrium without overshooting, in the shortest possible time after it has been displaced from equilibrium

Question 26

Heavy damping

Answer 26

Returns to equilibrium more slowly than the critical damping case

Question 27

Forced vibration

Answer 27

Vibrations of the system subjected to an external force

Question 28

Resonance

Answer 28

The amplitude of vibration of an oscillating system subjected to a periodic force is largest when the periodic force has the same frequency as the resonant frequency of the system

Question 29

Resonant frequency

Answer 29

The frequency of an oscillating system in resonance

Question 30

Applied frequency of the periodic force

Is equal to …

Answer 30

The natural frequency of the system

Question 31

Phase difference between displacement and the periodic force is …

Answer 31

1/2π

Question 32

Resonance ( lighter the damping)

Answer 32

Larger the maximum amplitude becomes at resonance

Closer the resonant frequency is to the natural frequency of the system

Question 33

Amplitude

Answer 33

Oscillations is the maximum displacement of the oscillating object. Form equlibrium

Question 34

free vibration

Answer 34

vibrations where the is no damping and no periodic force acting on the system, so the amplitude of the oscillations is constant

Question 35

sinusoidal curves

Answer 35

any curve with the same shape as a sine wave

Question 36

periodic force

Answer 36

a force that varies regularly in magnitude with a define time period

Question 37

applications of simple harmonic motion

Answer 37

T = KΔL
a = -kx / m
a = -Ψ^2x
(object would oscillate in a simple harmonic motion )

T=2π √ m/k

Question 38

what determines the frequency of oscillation of a loaded spring?

Answer 38

adding extra mass

using a weaker spring

Question 39

simple harmonic motion speed equation

Answer 39

(Ek=1/2mv^2)

v= ±√ (A^2 -x^2)

(x=0 would give the maximum speed)

Question 40

energy displacement graph

Answer 40

Ep = 1/2 kx^2

kinetic energy of inverted parabola
Ek = Et -Ep
= 1/2 k(A^2 -x^2)

Question 41

for a oscillating frequency system with little or no damping at resonance

Answer 41

the applied frequency of the periodic force = the natural frequency of the system

Question 42

bridge oscillations

Answer 42

bridges can oscillate because of the springs and it mass
a cross wind can form a force on a bridge, if the wind speed is such that the periodic force is equal to the natural frequency, resonate can occur
a steady trail of people in step with each other walking across a footbridge can cause resonant oscillations of the bridge span if there is not enough damping

Question 43

max speed

Answer 43

ωA

Question 44

max acceleration

Answer 44

ω^2 A