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
