Waves Flashcards
What is springs constant measured in
N/m
What is single harmonic motion
Displacement is proportional to and in the opposite direction to the acceleration
What direction is the restoring force
It is always opposite direction of the spring
At what point is the restoring force at it’d largest
At full length/ max extension
For the horizontal spring what equals eachother and derived it
T=F
-kx = ma (hookes and 2nd law)
a = d²x/dt² = -kx/m
How can hookes law be represented on a graph and where is the equilibrium
Sin/ cos
When y= 0
During hookes law what is force proportional too
Extention
When can SHM be observed on a mass on a string
When the surface is frictionless and If the spring is extended and released.
What will a mass oscillate around during SHM
Equilibrium y=o
The amplitude on a SHM graph at the displacement at the max or min
Maximum displacement
How can SHM and circular motion be linked
Through anglur frequency
Y=Asinwt is this natural or self made
Natural
Why is y=Asinwt natural
Because it is assumed that a vertical mass starts from equilibrium point and has a maximum amplitude and it moved on its own
What is the equation when we assume that the mass oscillates starting from a maximum amplitude A
y= Acoswt
Is y=Acoswt is self made or natural
Self-made
What is the period in relation too SMH
The period of SHM is the time taken to complete one oscillation
What is the frequency in relation too SHM
To the number of complete oscillation preformed per second
What are the two relationships needed too derive a relationship for velocity free from cos and sin.
V=dy/dt
sin²0+cos²0=1
Y=Asinwt
derive a relationship for velocity free from cos and sin
Differentiate y=Asinwt to get
V=Awcoswt
Make sin²wt+cos²wt=1 to get
coswt=square root of 1-sin²wt
Therefore v=+or- Aw squareroot 1-sin²wt
And we can arrange the original displacement equation to get
Y²/A²= sin²wt
Which would sub in to get
V=+or- Aw square root 1- y²/A²
Put over one fraction simplify and take our A
The simple harmonic graph of y against wt
Sin graph
The simple harmonic graph of y against wt. Where is the minimum velocity
At the maximum amplitude
The simple harmonic graph of y against wt, at what point at the velocity at a maximum
When y=0
How can we derive our linear equation for kinetic enegrry and the velocity equation for simple harmonic lotion
Sub v into the 1/2mv²
When velocity is at it’s maximum what is the knetic engery
It equals the total engery and meaning thr potential is zero
What happens to the 3ngery when y=+-A
All thr energy at potential energy at minimum velocity
What will happen to the kinetic enegery when it is oscillating
It will loose engery due to friction
What cause the fiction when a object is oscillating
Air
Rubbing
What happens to the amplitude of thr oscillation If the engery is decreasing
It will also decrease
What is damping in a system
It is described as the rate at which enegery is lost
Or
The rate at which the amplitude is decreasing
What is critical damping
It is the minimum amount of damping that completely eliminates the oscillation
What does a cental damping graph look like
A gradual cruve to 0
What is under damping
Is when the system returns to equilibrium quickly but overshoots and crosses the equilibrium position one or more times
What does the graph of under damping look like
The will curve under the t axis and yhrn back over until to reaches 0