Simple harmonic motion unit 4 Flashcards
how is angular velocity found? what are the units?
angular displacement / time. The units are radians/seconds.
what is the symbol for angular velocity?
ω
What is angular displacement measured in?
a number of π
The end of a piece of string rotates 5 times a second. The string is 50cm long. Find the linear speed.
1 revolution is 2π radians. Thus angular speed is 10π radians a second.
10π * 0.5=5π
What is the equation linking linear velocity, radius and angular velocity?
V=rω
What is frequency?
The number of revolutions per second.
What is the period?
time for 1 complete revolution.
Why does centripetal acceleration happen?
It happens due to a change in direction of motion even if it moves at constant speed.
What is centripetal force occur?
The resultant force on an object that makes an object move round a circular path. The force acts in the same direction as centripetal acceleration towards the center of the circle.
When swinging a mass on a vertical string, when is it more likely to break?
At the bottom. This is because the tension has to be equal to that of the sum of the centripetal force and gravity.
When swinging a mass on a vertical string, how is the tension found at the top, bottom and side?
At top centripetal force minus mg.
At the side just the centripetal force.
At the bottom centripetal force plus mg.
What is simple harmonic motion?
An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint and its directed towards the midpoint.
The time period is independent of the amplitude meaning it is isochronic.
What is the phase difference between a displacement and velocity time graph of an object showing SHM?
π/2.
The phase difference between velocity and acceleration is also π/2.
What is light or heavy damping?
Light. Will only lose a small amount of amplitude each time.
Heavy. Loses more amplitude each time.
What happens with damping?
Amplitude decays over multiple periods.
The period is not affected by damping.
It is exponential decay meaning the bigger the displacement, the bigger the decrease. One peak may be 0.8 times the last one and they always increase by a factor of 0.8
What is free oscillation?
Once displaced a system will oscillate at it’s natural frequency.
How does periodic driving force work?
It is applied to a system to make it oscillate. The frequency of the driving period force is equal to the natural frequency of the system.
Why doesn’t the amplitude increase to infinity with resonce?
Because damping will limit it.
What is conservation of momentum?
For a system of interacting species, the total momentum is constant, provided no external forces act.
what are the units for angular velocity?
radians per second.
In simple harmonic motion, how is displacement measured?
The distance from the midpoint to the object.
What is the restoring force in simple harmonic motion?
The force that always pulls or pushes the object to the midpoint.
What affects the size of the restoring force?
the displacement. The greater the displacement, the greater the force.
What provides the restoring force in a pendulum or in a mass on a spring?
gravity or elastic potential energy.
In SHM, what does the restoring force do to the object when moving towards and away from the midpoint ?
It does work to it, and transfers PE to KE when going towards it.
When going away, KE to PE.
when is KE at a maximum?
At the midpoint.
When is PE at a maximum?
At maximum displacement.
What is the mechanical energy?
The sum of the kinetic and potential energy. It stays constant unless there is damping.
what is the phase relationship between an acceleration and displacement time graph?
They are in anti phase.
What is a cycle in SHM
maximum positive displacement to maximum negative displacement and back.
is the period related to the amplitude?
No. This means that even if a pendulum swings become very small, they will still take the same time.
In the max accleration equation, what does the capital A mean?
the maximum displacement.
When a mass it attached to a horizontal spring and is moving around, how is the force calculated?
F=-kx
k is the spring constant. x is the displacement.
When does the pendulum show SHM?
Only with small oscillations. Up to about 10 degrees from the midpoint.
What is the natural frequency?
the frequency something oscillates at when left to its own devices.
What happens at resonance?
the phase difference between the driver and the oscillator is 90.
what is the phase relationship between the driving frequency and natural frequency ?
When the driving frequency is less than the natural frequency, they are in phase.
When it is faster there are completely out of phase.
when does resonance happen?
driving frequency = natural frequency.
When the frequency approaches resonance and goes past resonance, what happens to the amplitude?
It gets larger and then falls.
how does the damping affect the way in which resonance is reached?
If something is lightly damped, the amplitude will only increase when the driving frequency is close to the natural frequency and it will increase by a large amount.
With heavy damping, it isn’t as sensitive to the driving frequency and it doesn’t increase by as much.
what is the phase difference between a graph of particle velocity and particle displacement?
0.5pi
If you add mass to a pendulum, what happens to the damping ?
It will have more kinetic energy when oscillating and will lose about the same amount due to air resistance than without the mass so it is less heavily damped as a smaller proportion is lost
What are forced vibrations?
The driver forces the system to vibrate.
If the driving frequency is less than the natural frequency they are in phase
If the driving frequency is greater than the natural frequency, they are completely out of phase.
