17 - Oscillations

Question 1

simple harmonic motion is an oscillating motion where the…

Answer 1

acceleration is proportional to displacement
acceleration (and resultant force) always in opposite direction to displacement - towards equilibrium position

a∝-w^2x

Question 2

x=Asinwt

Answer 2

v=dx/dt = wAcoswt
max V when coswt = 1
max v =wA
max v = 2πfA

Question 3

a=-w^2x , what is max a

Answer 3

max a when x is max amplitude
so a max = -w^2A

Question 4

resonance is

Answer 4

amplitude of oscillation increases as driving frequency of external force applied is same as natural frequency of object
object oscillates at driving force frequency

(if undamped, amplitude will continue to increase until system fails)

Question 5

at resonance =

Answer 5

natural frequency of system is equal to the applied frequency of the periodic force (in phase)

Question 6

what does damping decrease (graph)

Answer 6

amplitude lower for all frequencies
max amplitude occurs at lower frequency than natural f
peak becomes flatter, broader, graph shifts to left

Question 7

natural frequency

Answer 7

frequency of a system oscillating without external periodic force

Question 8

periodic force

Answer 8

force with regularly changing amplitude and definite time period

Question 9

forced oscillation

Answer 9

oscillation under external periodic force, causing it to oscillate at a particular frequency

Question 10

when oscillation is at left

Answer 10

x = max (-)
v = 0
a = max (+)
F = max (+)

Question 11

when oscillation is at midpoint/equilibrium

Answer 11

x = 0
v = max (+/-)
a = 0
F = 0

Question 12

when oscillation is at right

Answer 12

x = max (+)
v = 0
a = max (-)
F = max (-)

Question 13

Vmax

Answer 13

Vmax = 2πfA

Question 14

a.max

Answer 14

a.max = -(2πf)^2 A
where x = a due to max displacement

Question 15

acceleration and force

Answer 15

are linked and both act towards equilibrium, opposite direction to displacement

Question 16

energy changes as mass spring system goes from lowest to highest point

Answer 16

KINETIC ENERGY - zero at lowest, increases to maximum at equilibrium then decreases to 0 at highest

GRAV POTENTIAL ENERGY - increases

ELASTIC POTENTIAL ENERGY - decreases

TOTAL ENERGY decreases due to damping effect of air, air gains thermal energy

Question 17

total energy is equal to

Answer 17

maximum kinetic energy

Question 18

the period of a simple harmonic oscillator…

Answer 18

is independent of its amplitude (isochronus oscillator - same time)

Question 19

what is a free oscillation

Answer 19

when an object oscillates at its natural frequency, without any eternal forces applied

Question 20

where is kinetic energy max

Answer 20

at equilibrium point, where velocity is a maximum

Question 21

where is maximum potential energy max

Answer 21

occurs at amplitude positions (max displacement).

Question 22

damping and energy

Answer 22

resistive forces reducing amplitude of oscillations
energy loss to resistive forces like drag and friction
kinetic energy of oscillations is transferred to other forms such as heat

Question 23

types of damping

Answer 23

light - naturally like oscillating in air - amplitude decreases, period unchanged

heavy - oscillating in water, amplitude decreases significantly

critical - oscillating in treacle, object stops before one oscillation, moves to equilibrium, no oscillatory motion

Question 24

use of damping

Answer 24

suspension forks on mountain bikes - damping uses to absorb energy of shock. if not, it would oscillate up and down

Question 25

frequency of free oscillation

Answer 25

= natural frequency of oscillation

Question 26

resonance and energy

Answer 26

at resonant frequency, greatest possible transfer of kinetic energy from driver to oscillator

Question 27

damping may reduce at a rate that is…

Answer 27

exponential - amplitude decreases by same factor in equal time intervals

Question 28

damping force is in what what direction to velocity
damping force is maximum when

Answer 28

opposite to velocity
max. when displacement is zero as speed is greatest so damping force is greatest in magnitude

Question 29

example of forced oscillation

Answer 29

loudspeaker oscillating and producing a continuous note

Barton’s pendulum - paper cones diff lengths suspended along with heavy brass bob - driving force making all cones oscillate at same frequency. the cone w same length as brass bob has same natural f so will resonant and have greater amplitude

Question 30

mass is hung from bottom of spring. explain how it can be made to show resonance

Answer 30

force mass to oscillate w/ periodic force. driving must equal natural frequency of mass-spring system, increasing amplitude of oscillation - resonance

Question 31

when does an oscillator dissipate maximum energy

Answer 31

at equilibrium - max speed so max kinetic energy and greatest friction

Question 32

experiment to obtain displacement/time graph for oscillating mass in lab

Answer 32

motion sensor connected to data logger to get info on displacement and time shown on connected computer
motion sensor placed close to mass to eliminate reflections from other objects

reflector should not cause damping
motion sensor should be directed along line of oscillation

Question 33

example of resonance

Answer 33

microwave oven - drving freq - em radiation which matches the natural freq of water molecules causing resonance. amplitude increases and kinetic energy of molecules in food increases

child on swing

wind and bridges