Topic 9: Wave phenomena (HL) Flashcards
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0cos(ωt)
acceleration
(a)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0
MAXIMUM acceleration
(amax)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0 sin(ωt);
(??) = ωx0 cos(ωt)
velocity
(v)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0
MAXIMUM velocity
(Vmax)
[DATA BOOKLET] Equation for [???] in SHM = x0 sin(ωt); = x0 cos(ωt)
displacement (x)
How do you know whether to use -sin(ωt) or cos(ωt) for velocity in SHM?
for SHM the derivation depends on the original displacement graph/function. [if displacement was sin(ωt) then velocity will be cos(ωt); if displacement was cos(ωt) then velocity will be -sin(ωt)]
How does the total energy of a system change during SHM?
it stays constant (total energy = kinetic energy + potential energy)
What is the shape of a displacement graph for simple harmonic motion (SHM)?
Sinusoidal
Write SHM as an equation
a = -(ω2)x
What is acceleration proportional to in SHM?
negative displacement (a ∝ -x)
What is the restoring force in a simple pendulum?
m⋅g⋅sinθ
What is x0?
maximum displacement (amplitude)
When in kinetic energy maximum in SHM?
displacement = 0; x = 0
When in kinetic energy minimum in SHM?
at maximum displacement (amplitude)
x = x0
When in potential energy maximum in SHM?
displacement = x0; at maximum displacement (amplitude)
When in potential energy minimum in SHM?
displacement = 0
x = 0
In what direction does the acceleration in SHM act?
Towards the equilibrium point
(x=0)
What is ω and its unit?
angular frequency
rad s-1
How do you identify if SHM is taking place?
- Identify forces when object is displaced from rest position (free-body diagram)
- Calculate resultant force using Newton’s second law: if the force is proportional to displacement and the direction is always towards rest position, then there is SHM.
- ω2 = (restoring force per unit displacement/mass)
Assumptions for SHM (vertical spring)
- mass of spring is negligible (compared to the mass of load)
- friction (air friction) is negligible
- spring obeys Hooke’s law at all times (elastic limit is not exceeded)
- gravitational field strength, g, is constant
- the spring’s fixed end cannot move
Assumptions for SHM (simple pendulum)
- mass of the pendulum is negligible compared to that of the load
- friction (air friction) is negligible
- the maximum angle of swing is small (≤ 5
[DATA BOOKLET]
What does each symbol mean and what is its unit?
ω = 2π/T
ω is angular frequency, in rad s-1
T is time period, in s
Equation for velocity in SHM (no trig functions)
v = ±ω√( x02 - x2 )
If displacement follows a positive sin function, what functions will velocity and acceleration follow?
x = sin ωt
v = cos ωt
a = -sinωt
[NOTE: these are not the full equations, just the trig function part]