Simple Harmonic Motion Flashcards
What is simple harmonic motion?
Simple harmonic motion is a type of motion that occurs when acceleration is directly proportional to the displacement from a fixed point, and is always in the direction of that fixed point.
What are the 2 requirements for a body to be in simple harmonic motion?
1) The acceleration of the body is always directed to the fixed point
2) The acceleration of the body is directly proportional to the displacement from the fixed point
What is the equation of simple harmonic motion?
a = -ω^2x
As a body is in SHM when does it’s acceleration increase?
When it’s displacement from the equilibrium position increases.
As a body is in SHM when does it’s velocity increase?
When it’s displacement from the equilibrium position decreases.
What is the equation for displacement of a body in SHM starting at the extremity?
x = Acos(ωt)
What is the equation for displacement of a body in SHM starting at the equilibrium?
x = Asin(ωt)
How is velocity found using the equations of displacement?
But differentiating the displacement equation
What is the equation of maximum velocity?
V = Aω
What is the equation of finding the period of the mass in a spring?
T = 2π√m/k
What is the equation for the period in a pendulum?
T = 2π√l/g
What is the energy equation for maximum KE?
kE = (1/2)m(ωA)^2
What is the energy relation in oscillation?
As the body moves towards the extremity, it’s potential energy increase whereas it’s kinetic energy decreases. However as the body moves towards equilibrium it’s potential energy decreases and its kinetic energy increases. Within SHM this conversion of energy is constantly occurring.
What are free oscillations?
Free oscillations are oscillations which are unaffected by external forces or actions as there are no dissipative forces acting on them causing their amplitude to be consistent
What are forced oscillations?
Forced oscillations are are oscillations produced by the action of a periodic driving force
What is damping?
Damping means that the total energy of the oscillation is being reduced and this is done by resistive forces that are in the opposite direction. They cause energy to be absorbed from the system.
What is light damping?
Light damping is where the energy of the system gradually decreases overtime therefore the amplitude decreases overtime and the period is unaffected
What is heavy damping?
Heavy damping is where a system is set into oscillation but takes a long time to return to equilibrium, and it will never complete a full oscillation
What is critical damping?
Critical damping is when a system is displaced but not set into oscillation and returns to equilibrium in a quarter of a period with no or little overshoot
Where is critical damping used?
In car systems or bike suspensions
What is resonance?
Resonance is when the frequency of the driving force matches the natural frequency of the system causing the system to absorb energy and therefore creating a maximum in the amplitude of oscillation
Where is resonance useful?
In microwaves, as the frequency of the microwave is similar to the natural frequency of the water molecules allowing food to heat up
Where is resonance useless?
On bridges, as if the frequency of people walking matches the natural frequency of the bridge, it can cause the bridge to oscillate too much
What is the effect of damping on natural frequency?
- The amplitude of peak oscillation decreases (effect decreases further away from resonance)
- The resonance peak gets broader
- The frequency as which maximum response occurs also decreases
