6.1: Further Mechanics Flashcards
What are forced vibrations?
-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
What happens to resonance with increased damping?
-Value of peak decreases
-Peak broadens
-Peak occurs at a lower natural frequency
What are free vibrations?
-The frequency at which the system tends to vibrate at
-Also known as the natural frequency
What is resonance?
-Resonance is when much larger amplitudes are produced
When does resonance occur?
-Resonance occurs when the frequency of the system is the same as the natural frequency of the same system
What are the phase differences for resonance?
-At resonance the phase difference is π/2
-Above resonance the phase difference is π
How can resonance be danegrous?
-Crosswinds and large groups of people walking across bridges can cause resonance and cause damage to the structure
What is critical damping?
-When the system returns to the equilibrium position in the shortest time without overshooting
What is damping?
-Damping is when energy is taken out of the system reducing the energy per cycle
How does the kinetic energy graph for SHM look?
-It is an inverted parabola
-Ek=(1/2)k(A^2-x^2)
How does the potential energy graph for SHM look?
-It is parabolic
-Ep=(1/2)kx^2
How are potential energy and kinetic energy related for SHM?
-Potential energy is a maximum when the kinetic energy is a minimum
-Kinetic energy is a maximum when the potential energy is a minimum
What is the definition of simple harmonic motion?
-The acceleration is directly proportional to the displacement but in the opposite direction
-Acceleration acts towards the equilibrium point
What are the equations for simple harmonic motion?
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
What is the time period for a pendulum?
T=2π.√ (l/g)
Where:
T=time period
l=length
g=acceleration due to gravity
What is the frequency for a pendulum?
f=(1/2π).√ (g/l)
Where:
f=frequency
l=length
g=acceleration due to gravity
What is the time period for a mass spring system?
T=2π.√ (m/k)
Where:
T=time period
m=mass
k=spring stiffness
What is the frequency for a mass spring system?
f=(1/2π).√ (k/m)
Where:
f=frequency
m=mass
k=spring stiffness
How do you convert from degrees to radians?
-Multiply by π/180
What force keeps an object in a circular path at a constant speed?
-The centripetal force
-Acts inwards towards the centre of the circular path
How do you calculate angular speed?
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
How do you calculate centripetal force?
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
How do you calculate centripetal acceleration?
a=(ω^2)*r
ω=v/r
so a=(v^2)/r
Information that can’t be put on flashcards
-Displacement-time graph for SHM
-Velocity-time graph for SHM
-Acceleration-time graph for SHM
-Graphs for different types of damping
What is the equation for energy in a mass spring system?
E= (1/2)mω^2*A^2
