chapter 17 - oscillations

Question 1

shm demo spring and mass system

Answer 1

motion sensor connected to data logger and computer - under a spring with a mass attached oscillating
motion sensor - signal of known speed emitted then detected, time taken for echo to return is measured, distance = speed*time - must be in plane of motion, creates a movement plot

Question 2

displacement (x)

Answer 2

distance from equilibrium position (m)

Question 3

amplitude (A)

Answer 3

maximum displacement from equilibrium position (m)

Question 4

period (T)

Answer 4

time taken for one full oscillation (s)

Question 5

frequency (f)

Answer 5

no. oscillations per unit time (Hz)

Question 6

angular frequency (⍵)

Answer 6

2𝞹/T = 2𝞹f
rad/sec

Question 7

definition of shm

Answer 7

• acceleration is proportional to displacement
• acceleration acts in the opposite direction to the displacement
  (restoring force always acting towards equillibrium)
  a ∝ -x
  a = -⍵x

Question 8

isochronous

Answer 8

time period is independent of amplitude
- bigger A = bigger acceleration so faster over bigger distance = same T

Question 9

equations of shm

Answer 9

⍵ = 2𝞹/T = 2𝞹f
x = Acos⍵t or Asin⍵t - cos if start at max displacement or sin is start at equilibrium
v = +- ⍵√A² - x²
vmax = +- ⍵A
a = -⍵²x

Question 10

energy of shm

Answer 10

total energy is constant
PE goes from max to min at equilibrium to max
KE goes from min to max at equilibrium to min
EPE = 1/2kx²
KE = 1/2k(A²-x²)

Question 11

damping

Answer 11

has the effect of reducing the amplitude of oscillations by applying an external force

Question 12

damping examples

Answer 12

• air resistance bringing a mass-spring system to a stop
• shock absorbers in bike breaks increasing time to stop
• fire doors gave dampers so they shut at a controlled rate

Question 13

3 types of damping

Answer 13

• light damping
• heavy damping
• critical damping

Question 14

light damping

Answer 14

• period remains unchanged (isochronous)
• amplitude gradually decreases with time

Question 15

heavy damping

Answer 15

• same as light but amplitude decreases more quickly

Question 16

critical damping

Answer 16

no oscillations occur

Question 17

free oscillations

Answer 17

• when a system is displaced from equilibrium position and oscillates without external forces
• this oscillation frequency is known as natural frequency
  eg pendulum on string

Question 18

forced oscillations

Answer 18

• when a system is driven by a periodic driving force
• the frequency of that driving force is known as the driving frequency
  eg child moving legs on a swing

Question 19

bartons pendulum experiment

Answer 19

penulum A provides a driving frequency that matches the natural frequency of pendulum B - as they are the same length
therefore moves with greater amplitude

Question 20

real life examples of free and forced oscillations

Answer 20

• microwaves - microwaves (driving), water molecules (natural)
• MRI scanners - magnetic field (driving), water molecules in body (natural)
• ground resonance helicopters - rotor blade (driving), ground (natural)

Question 21

resonance

Answer 21

when the driving frequency matches the natural frequency a system will resonate
causing amplitude of oscillations to increase
- undamped system will increase in amplitude as freq increase until natural (max) then decreases
- damped system will do the same but with a lower peak and moved left

Question 22

amplitude that decays exponentiallys

Answer 22

if measured at the same time interval then the ratio between the displacement at those intervals is constant

Question 23

resonance eg

Answer 23

eg paper on a mass spring system will have a lower natural freq and lower resonance peak then a normal mass spring system

Question 24

shm graphs

Answer 24

start with displacement
acceleration is opposite displacement
velocity is the same as displacement but shifted to start at the opposite eg peak if displacement started at eq or eq is displacment started at peak