6.1: Further Mechanics

Question 1

What are forced vibrations?

Answer 1

-A driving force causes the system to vibrate at a different frequency
-For higher driving forces the phase difference is π
-For lower driving forces there is no phase difference
-At resonance the phase difference is π/2

Question 2

What happens to resonance with increased damping?

Answer 2

-Value of peak decreases
-Peak broadens
-Peak occurs at a lower natural frequency

Question 3

What are free vibrations?

Answer 3

-The frequency at which the system tends to vibrate at
-Also known as the natural frequency

Question 4

What is resonance?

Answer 4

-Resonance is when much larger amplitudes are produced

Question 5

When does resonance occur?

Answer 5

-Resonance occurs when the frequency of the system is the same as the natural frequency of the same system

Question 6

What are the phase differences for resonance?

Answer 6

-At resonance the phase difference is π/2
-Above resonance the phase difference is π

Question 7

How can resonance be danegrous?

Answer 7

-Crosswinds and large groups of people walking across bridges can cause resonance and cause damage to the structure

Question 8

What is critical damping?

Answer 8

-When the system returns to the equilibrium position in the shortest time without overshooting

Question 9

What is damping?

Answer 9

-Damping is when energy is taken out of the system reducing the energy per cycle

Question 10

How does the kinetic energy graph for SHM look?

Answer 10

-It is an inverted parabola
-Ek=(1/2)k(A^2-x^2)

Question 11

How does the potential energy graph for SHM look?

Answer 11

-It is parabolic
-Ep=(1/2)kx^2

Question 12

How are potential energy and kinetic energy related for SHM?

Answer 12

-Potential energy is a maximum when the kinetic energy is a minimum
-Kinetic energy is a maximum when the potential energy is a minimum

Question 13

What is the definition of simple harmonic motion?

Answer 13

-The acceleration is directly proportional to the displacement but in the opposite direction
-Acceleration acts towards the equilibrium point

Question 14

What are the equations for simple harmonic motion?

Answer 14

x=A.cos(ω.t)
v=-A.ω.sin(ω.t)
a=-A.w^2.cos(w.t)

a=-ω^2.x

Max x= A
Max v= A.ω
Max a= A.ω^2

Question 15

What is the time period for a pendulum?

Answer 15

T=2π.√ (l/g)
Where:
T=time period
l=length
g=acceleration due to gravity

Question 16

What is the frequency for a pendulum?

Answer 16

f=(1/2π).√ (g/l)
Where:
f=frequency
l=length
g=acceleration due to gravity

Question 17

What is the time period for a mass spring system?

Answer 17

T=2π.√ (m/k)
Where:
T=time period
m=mass
k=spring stiffness

Question 18

What is the frequency for a mass spring system?

Answer 18

f=(1/2π).√ (k/m)
Where:
f=frequency
m=mass
k=spring stiffness

Question 19

How do you convert from degrees to radians?

Answer 19

-Multiply by π/180

Question 20

What force keeps an object in a circular path at a constant speed?

Answer 20

-The centripetal force
-Acts inwards towards the centre of the circular path

Question 21

How do you calculate angular speed?

Answer 21

ω=2πf
ω=2π/T as f=1/T

ω=v/r

Where:
ω=angular speed
f=frequency
T=time period
v=tangential velocity
r=radius

Question 22

How do you calculate centripetal force?

Answer 22

F=ma
a=(v^2)/r

So F= (mv^2)/r
Also F=m(ω^2)*r

Where:
F=force
a=acceleration
v=tangential velocity
r=radius
m=mass
ω=angular speed

Question 23

How do you calculate centripetal acceleration?

Answer 23

a=(ω^2)*r

ω=v/r
so a=(v^2)/r

Question 24

Information that can’t be put on flashcards

Answer 24

-Displacement-time graph for SHM
-Velocity-time graph for SHM
-Acceleration-time graph for SHM
-Graphs for different types of damping

Question 25

What is the equation for energy in a mass spring system?

Answer 25

E= (1/2)mω^2*A^2