Further Mechanics

Question 1

Simple Harmonic oscillation definition

Answer 1

An oscillation in which the acceleration of the object is directly proportional to its displacement from it’s equilibrium position, and is directed towards the equilibrium

Question 2

SHM velocity equation

Answer 2

V= ω sqrt(A^2-X^2)

Question 3

SHM velocity equation

Answer 3

V= ω sqrt(A^2-X^2)

Question 4

Maximum velocity equation

Answer 4

Vmax= ωA

Question 5

Maximum velocity equation

Answer 5

Vmax= ωA

Question 6

Displacement equation

Answer 6

x=Acos(ωt)

Question 7

Acceleration equation

Answer 7

A=-ω^2 x
Amax= ω^2A

Question 8

Angular velocity (ω) equation

Answer 8

ω=2πf=2π/T

ω=V/r

ω= θ/t

Question 9

What is the total energy equal to at the equilibrium

Answer 9

Maximum kinetic energy

Question 10

What is the total energy equal to at the amplitude

Answer 10

Maximum potential energy

Question 11

Centripetal acceleration equation

Answer 11

a= ω^2 r
a=v^2 / r

Question 12

Centripetal force equation

Answer 12

F=mω^2r
F=mv^2/r

Question 13

What happens when something moves in a circular path and the centripetal force is removed?

Answer 13

The object will fly off at a tangent

Question 14

Time period for a simple pendulum
Time period for a mass-spring system

Answer 14

T=2π sqrt(l/g)
T=2π sqrt(m/k)

Question 15

What can the time period equation for simple pendulums be used

Answer 15

Only for small oscillations
Angles under 10 degrees

Question 16

What is the centripetal force of an object equal to at the TOP of a vertical circle

Answer 16

F=T+W

Question 17

What is the centripetal force of an object equal to at the BOTTOM of a vertical circle

Answer 17

F=T-W

Question 18

Free vibration

Answer 18

-Involves no transfer of energy to or from surroundings
-Objects oscillate at resonant(natural) frequency

Question 19

Forced vibration

Answer 19

-External driving force that’s periodic
-Applied at driving frequency

Question 20

Forced vibration

Answer 20

-External driving force that’s periodic
-Applied at driving frequency

Question 21

What is resonance?

Answer 21

-When the driving frequency = natural frequency
-Maximum energy transfer
-Rapid/dangerous increase in amplitude

Question 22

When the driving frequency is less than natural frequency, what is the amplitude and phase difference(between driver and oscillator)

Answer 22

Amplitude= same as driver
Phase difference= 0 (in phase)

Question 23

When the driving frequency is the same as the natural frequency, what is the amplitude and phase difference(between driver and oscillator)

Answer 23

Amplitude= Very large
Phase difference= π/2

Question 24

When the driving frequency is greater than natural frequency, what is the amplitude and phase difference(between driver and oscillator)

Answer 24

Amplitude= small
Phase difference= π

Question 25

What is damping?

Answer 25

Oscillator experiences resistive force that removes energy from it

Always acts in the opposite direction to motion

Question 26

With what types of damping does the time period not change?

Answer 26

Light and heavy

Question 27

How does damping affect amplitude?

Answer 27

It can reduce it but not stop it completely

Question 28

Why is acceleration proportional to negative displacement?

Answer 28

Because it is always directed towards the equilibrium

Question 29

What effect does damping have on resonance?

Answer 29

No effect
Damping just reduces amplitude

Question 30

What are 2 measures to reduce size of oscillations

Answer 30

Use shock absorbers
Use a material with a high natural frequency

Question 31

Displacement against time graph

Answer 31

Cos graph

Question 32

Velocity against time graph

Answer 32

Negative sin graph

Question 33

Acceleration against time graph

Answer 33

Negative cos graph

Question 34

Velocity against amplitude graph

Answer 34

Circle

Question 35

Acceleration against amplitude graph

Answer 35

Straight line negative through origin

Question 36

Phase difference when resonance happens

Answer 36

Pi/ 2