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.