Chapter 15- Oscillations Flashcards
Amplitude
Max displacement from the equilibrium position
In metres
Period
The time taken to complete one oscillation T
In seconds
Frequency
The number of complete oscillations per second
In Hz
Two types of oscillations
- pendulum
* spring
Period, frequency eq
F= 1/T
Simple harmonic motion is
The periodic motion about an equilibrium position such that acceleration (Fresultant=ma)is:
• proportional to the displacement
• always directed towards the fixed point
SHM equation
F= -kx (k is a constant)
F is always opposite in direction to displacement
F= -kx equation becomes
a= -w^2 x
SHM oscillation period equation
T= 2pie ✅m/k
Simple pendulum
What does simple mean?(2)
- small, dense pendulum bob
* light inextensible string
SHM oscillation equation for period on a pendulum
T= 2pie✅L/g
L= length of string from attached point G= grav
Graph of -w^2A against x
= a negative straight line
= inversely proportional
Equations regarding x= and v=
X= Acoswt
V= -wAsinwt
Displacement for pendulum bob
Always from the equilibrium point
In oscillation velocity is at max when…
In the central position
In oscillation velocity is 0 when..
At the end of the oscillation
When displacement is at maximum (+ve/-ve)
Gradient is zero
The gradient of a velocity time graph
Acceleration
Acceleration eq combing all the others
a= -w^2Acoswt
Because differentiate sin and you get cos
v= -wAsinwt x= Acoswt a= -w^2x
w equation
w= 2pie f
Or
w= 2pie/ T
As a pendulum swings to and fro there is a continuous interchange of
Kinetic and gravitational potential energy
Potential energy at max when
Pendulum is at max displacement
Pendulum has max KE when
In central equilibrium position
Interchange between PE and KE is repeated _____ every oscillation
Twice every oscillation
From eq v= -wAsinwt
Max velocity value will be when sinwt = +1/-1
Giving…
Vmax= +/- wA
Max KE is when…
Equation is therefore…
When V is at its max
KE= 1/2 mv^2 = 1/2 m( -wA)^2
= 1/2 mw^2A^2
Law of conservation of energy means that within an oscillation
E kinetic + E potential = E total
Curve for both on graph
Happy face and sad face
Free oscillation def
One which no external force acts on the oscillating system except forces that give rise to the oscillation
Damped oscillation def
One in which energy is being transferred to surroundings resulting in oscillations of reduced amplitude and energy
Forced oscillations
Occur if force is continually applied to keep oscillation going
Same frequency as vibrating source
Not at own natural frequency
The damping graph shape is
Exponential
Can take log of it and plot to find straight line
Or look at ratios
A pendulum of the same natural frequency will absorb
The most energy and will be forced to oscillate with much larger amplitude
= called resonance
Resonance def
Oscillating system is forced to oscillate by an outside source at a frequency the same as its own natural frequency
Maximum energy transfer or energy resonance always occurs at
The natural frequency
If there is no damping
Then max amplitude resonance occurs when driving frequency is equal to the natural frequency of vibration of the mass
If there is damping
The resonant frequency at which amplitude is max is lower than the natural frequency
Difference increases as damping increases
