13p2 Oscillations Flashcards
What is the condition for simple harmonic motion (SHM)?
SHM occurs when there is a restoring force that is directly proportional to displacement and directed towards the equilibrium position
What is the formula for the restoring force in SHM?
F = -kx where F is the restoring force k is a system constant and x is displacement
What does the constant k represent in SHM?
The constant k represents the stiffness of the system such as the spring constant in a spring
What is amplitude in SHM?
Amplitude is the maximum displacement from the equilibrium position during oscillations
What is the time period (T) of an oscillation?
Time period is the time taken for one complete oscillation of the system
What is the restoring force in a simple pendulum?
The restoring force is the horizontal component of gravity acting on the pendulum bob
in SHM equations, what does A, ω, x, v and a mean with units
A - amplitude of oscillation (m)
ω - angular frequency (rad/s)
x - displacement from equilibrium position (m)
v - velocity (m/s)
a - acceleration (m/s^2)
What does T, l, g, m and k mean in simple harmonic oscillator questions with units
T - time period (s)
l - length of the pendulum (m)
g - gravitational acceleration (m/s^2)
m - mass (kg)
k - spring constant (N/m)
What does a displacement-time graph for SHM look like?
A sine or cosine wave with amplitude A and period T
How is velocity related to displacement in SHM?
Velocity is the gradient of the displacement-time graph and is maximum at equilibrium
When is velocity maximum in SHM?
Velocity is maximum when displacement is zero which is at the equilibrium position
What does a velocity-time graph look like in SHM?
A sine wave that is out of phase with displacement and peaks when displacement is zero
How is acceleration related to displacement in SHM?
Acceleration is directly proportional to the negative of displacement showing a restoring force
What is resonance?
Resonance is when a system is driven at its natural frequency causing a large increase in amplitude so when the driving frequency is equal to the natural frequency of the system
Give an example of resonance in real life.
Swinging on a swing when pushed at the right frequency, musical instruments and radios
What is the driving frequency?
The driving frequency is the frequency of the external force applied to the oscillating system
What is damping?
Damping is the loss of energy from an oscillating system due to resistive forces reducing amplitude over time
How does energy transform in SHM?
Energy transforms between kinetic and potential forms with total energy remaining constant in undamped systems
What is an undamped system?
An undamped system has no energy loss so amplitude and total mechanical energy stay constant
What is a damped system?
A damped system experiences energy loss to the environment resulting in decreasing amplitude
What are free vibrations?
Free vibrations occur when a system oscillates at its natural frequency without continuous external force
What are forced vibrations?
Forced vibrations occur when a system is driven by an external periodic force
What happens when driving frequency equals natural frequency?
Resonance occurs and the system’s amplitude becomes very large
What are the three types of damping?
Light damping critical damping and heavy damping each reducing amplitude differently
What is light damping?
Light damping or underdamping is when amplitude decreases slowly with each oscillation
What is critical damping?
Critical damping brings the system to rest in the shortest time without oscillating
What is heavy damping?
Heavy damping or overdamping slows the return to equilibrium without oscillations and takes longer than critical damping
How does damping affect resonance?
Damping lowers the resonant frequency reduces maximum amplitude and broadens the resonance curve
What is ζ (zeta) in damping?
Zeta is the damping ratio with ζ = 1 indicating critical damping less than 1 is underdamped and greater than 1 is overdamped
How do ductile materials reduce oscillation amplitude?
Ductile materials absorb energy through plastic deformation which reduces kinetic energy and amplitude
Why are climbing ropes designed to be ductile?
Climbing ropes deform plastically to absorb energy and critically damp oscillations for safety during a fall
Can a climbing rope be reused after a fall?
No because the plastic deformation permanently damages the rope’s structure making it unsafe
How to determine the value of an unknown mass using the resonant frequencies of the oscillation of known masses
1) hang a number of masses to the end of a spring
2) extend the spring up to the position of the fiducial marker - release it and start the stopwatch
3) measure time for 10 oscillations, use fiducial mark on clamp stand to improve accuracy
4) repeat process several times and find mean time period
5) vary number of masses and record time period for each condition
6) T^2 (y axis) against mass and draw line with best fit
since t^2 = m(k/4pi^2) so t^2 is proportional to m
7) attach an unknown mass to the end of spring and record time period then use graph to find mass
In the experiment to determine the value of an unknown mass using the resonant frequencies of the oscillation of known masses, how are errors reduced
finding 10 oscillations then dividing by 10 reduces percentage uncertainty
use a vernier motion tracker and data logger to find a more accurate value for time period removing human error and parallax error from fiducial mark
