further mechanics

Question 1

what’s simple harmonic motion?

Answer 1

an oscillation in which the acceleration of an object is directly proportional to its displacement from its equilibrium position, and is directed towards the equilibrium

Question 2

how would we draw the graphs for displacement, acceleration and velocity against time for SHM?

Answer 2

displacement- cosine or sine wave with a maximum value of A (amplitude)
velocity- maximum of wA, when the gradient of the displacement time graph is 0 velocity is 0
acceleration- maximum is w^2(A), when gradient of velocity time graph is a maximum, acceleration is maximum, opposite to displacement graph, inversed.

Question 3

whats phase difference?

Answer 3

how much one wave lags behind another

Question 4

what’s the phase difference for two waves in phase?

Answer 4

2pi radians or 0

Question 5

whats the phase difference between a velocity-time graph and a displacement time graph for SHM?

Answer 5

1/2 pi radians

Question 6

what’s the amplitude of an oscillation for SHM?

Answer 6

the maximum magnitude of the displacement

Question 7

what happens to the type of energy in all different stages of SHM?

Answer 7

as the object moves towards the equilibrium position, potential energy goes to kinetic
when the object is moving away from the equilibrium position, kinetics energy transfers back to potential
at equilibrium position, potential energy is 0 and kinetic is a maximum
at maximum displacement, kinetic energy is 0 and potential energy is at a maximum

Question 8

what is mechanical energy?

Answer 8

the sum of potential and kinetic energy

Question 9

what are simple harmonic oscillators?

Answer 9

systems that oscillate with simple harmonic motion

Question 10

what are the two types of simple harmonic oscillators that we need to know?

Answer 10

masses on springs and pendulums

Question 11

how is a mass on a string a simple harmonic oscillator?

Answer 11

when the mass is pushed or pulled either side of the equilibrium position, there is a restoring force exerted on it

Question 12

how can you work out the restoring force on a mass on a spring?

Answer 12

hooke’s law F=k x extension
or F= -k x displacement

Question 13

whats the equation to work out the frequency of a mass oscillating on a spring?

Answer 13

f= (1/(2pi)) x squareroot (m/k)

Question 14

whats the equation to work out the time period of a mass oscillating on a spring?

Answer 14

T= 2pi x squareroot (m/k)

Question 15

investigating the mass-spring system RP7- process

Answer 15

attach a trolley to a spring, pull it to one side by a certain amount then let it go

the trolley will oscillate back and forth as the spring pulls and pushes it in each direction
you can measure the time period by getting a computer to plot a displacement-time graph from a data logger connected to a position sensor

Question 16

what are the three variables you can investigate by using a mass-spring system?

Answer 16

mass, spring content, amplitude

Question 17

mass-spring system with variable as mass experiment RP7

Answer 17

change the mass by loading the trolley with masses
T^2 against mass graph as they should be directly proportional

Question 18

mass-spring system with variable as spring content experiment RP7

Answer 18

change the spring constant by using different combinations of springs
plot a graph T^2 against 1/k as they should be directly proportional

Question 19

mass-spring system with variable as amplitude experiment RP7

Answer 19

change the amplitude by pulling the trolley across by different amounts
plot T against A, T should remain constant as A increases

Question 20

what’s the equation to work out the acceleration for a simple pendulum?

Answer 20

a= -g x ø (in radians)

a= -g x (arc length/ radius)

Question 21

simple pendulum experiment RP7

Answer 21

attach a simple pendulum to an angle sensor and computer
use to computer to plot a displacement time graph and read off time period from this
you can change one variable at a time and see what happens
should show T^2 directly proportional to length

OR

hang the pendulum from a clamp and timing the oscillations using a stopwatch, use a fiducial marker

Question 22

what are other examples of demonstrating SHO other then mass-spring systems and simple pendulums?

Answer 22

U-tube containing some water
when at equilibrium, the levels of the water on either side of the tube are equal. when the pressure is then released, water undergoes SHO

Question 23

how does a U-tube show SHO for water?

Answer 23

to start the SHO water is displaced at maximum displacement
period of oscillation can be found through consideration of energy
as the mater oscillated, it will exchange KE and PE
at the equilibrium position, the KE will be at a maximum and PE will be 0

Question 24

what are free vibrations?

Answer 24

they involve no energy transfer to or from the surroundings

Question 25

if free vibrations occur, what type of frequency will a mass on a spring oscillate at?

Answer 25

its resonance frequency/ natural frequency

Question 26

what are forced vibrations?

Answer 26

they happen when there's an external driving force

Question 27

what is the driving frequency?

Answer 27

the frequency of the periodic external force that causes a system to be forced to vibrate

Question 28

what happens if the driving frequency is much less than the natural frequency?

Answer 28

then the two waves are in phase

Question 29

what happens if the driving frequency is much greater than the natural frequency?

Answer 29

the oscillator won't be able to keep up- the driver will be completely out of phase with the oscillator

Question 30

when is the mass-spring system resonating?

Answer 30

when the driving force approaches the natural frequency, the system gains more energy from the driving force and so vibrates with a rapidly increasing amplitude

Question 31

at resonance, what is the phase difference between the driver and the oscillator?

Answer 31

90 degrees

Question 32

how can you investigate the relationship between amplitude and driving frequency?

Answer 32

use a vibration generator to oscillate a mass-spring system, signal generator sets driving frequency, mass oscillates with very large amplitude at resonant frequency draw a graph amplitude-driving frequency amplitude is highest at natural frequency

Question 33

what are some examples of resonance?

Answer 33

radio is tuned so the electric circuit resonates at the same frequency as the radio station you want to listen to glass resonates when driven by a sound wave at the right frequency the column of air resonates in an organ pipe, driven by the motion of air at the base. this creates a stationary wave in the pipe a swing resonates if its driven by someone pushing it at its natural frequency

Question 34

what are damping forces?

Answer 34

forces that dissipate the energy of the oscillator to its surroundings eg. frictional forces like air resistance

Question 35

how does damping effect amplitude of oscillations?

Answer 35

damping reduces the amplitude of the oscillation over time, the heavier the damping the quicker the amplitude is reduced to zero (not including over damping)

Question 36

what is critical damping?

Answer 36

reducing the amplitude in the shortest possible time

Question 37

example of critical damping

Answer 37

car suspension systems are critically damped so they don't oscillate but return to equilibrium as quickly as possible

Question 38

what is overdamping?

Answer 38

they take longer to return to equilibrium than a critically damped system

Question 39

what's an example of overdamping?

Answer 39

some heavy doors that close down slowly, giving people time to walk through

Question 40

what also effects the amplitude of oscillations in the same way as damping?

Answer 40

plastic deformation of ductile materials

Question 41

how does the degree of damping effect the sharpness of the peak in amplitude?

Answer 41

lightly damped systems have a sharper peak in amplitude

Question 42

what experiment can you use to demonstrate effects of damping on the resonance of a spring-mass system?

Answer 42

attach a flat disc to the spring mass set up with a signal and vibration generator as the mass oscillates, air resistance on the disc acts as a damping force, reducing the amplitude of the oscillation. the larger the disc, the larger the damping force and the smaller the amplitude of oscillation of the system at resonance

Question 43

what is angular speed?

Answer 43

the angle an object rotates through per second

Question 44

how can you work out arc length with radians?

Answer 44

radius x angle