lectures

Question 1

hookes law

Answer 1

F=-kx x=displacement k=spring constant

Question 2

what force does hookes law describe

Answer 2

force used to stretch spring / restoring force towadrs equilibrium

Question 3

equation of motion for undamped shm for mass on spring

Answer 3

a= -(k/m)x

Question 4

shm equation

Answer 4

a=-omega^2x

Question 5

solution to shm equation

Answer 5

x=A cos(omega t +phi) but only when omega=(k/m)^-1/2

Question 6

to find equation of resonant frequency for mass on spring

Answer 6

omega=(k/m)^-1/2 f=(1/2pi)(k/m)^-1/2

Question 7

shm phase relations between displacement acceleration and velocity

Answer 7

velocity lags pi/2 behind displacement and acceleration lags pi/2 behind velocity

Question 8

potential energy for shm

Answer 8

kx^2/2

Question 9

total energy for shm

Answer 9

E=ke+1/2kx^2= kA^2/2

Question 10

damping force equation

Answer 10

F=-bv

Question 11

equation of motion for a damped system

Answer 11

ma + bv+ kx=0

Question 12

solution to damped harmonic motion

Answer 12

x=Cexp(alpha t)

Question 13

solved equation of motion

Answer 13

x= C exp(-bt/2m) 1 exp(sqrt(b^2/4m^2 -k/m)t)

Question 14

damping term of equation of motion

Answer 14

b^2/4m^2

Question 15

stifness term of equation of motion

Answer 15

-k/m

Question 16

when the system is heavily damped

Answer 16

damping term dominates- dead beat motion ocurs - non oscilatory motion b^2/4m^2 > k/m

Question 17

critical damping

Answer 17

when b^2/4m^2 = -k/m system returns to zero a in min time. non oscilatory motion

Question 18

light damping

Answer 18

decaying oscilatory motion b^2/4m^2 < k/m

Question 19

light damping equation

Answer 19

x= Cexp(-bt/2m).exp(j omega’ t) where omega’ = sqrt(k/m -b^2/4m^2)

Question 20

light damping equation real part

Answer 20

x=Cexp(-bt/2m). cos(omega’t +0)

Question 21

logarithmic decrement

Answer 21

the natural log of the ratio of the amplitudes of any two successive peaks

Question 22

logarithmic decrement equation

Answer 22

ln(x0/x1)=bT’/2m T’=2pi/omega’

Question 23

mechanical impedence

Answer 23

complex quantity that represents the resistance of a system to a force that gets it moving

Question 24

mechanical impedence equation

Answer 24

F/v = b+j(omega m +t)

Question 25

forced oscilation equation of motion

Answer 25

ma+mv+kx=Fcos(omega t)=Fexp(jomegat)

Question 26

forced oscilation equation of motion solution

Answer 26

-jFexp(j(omega t - phi)/omega |Z|

Question 27

analysis of forced shm

Answer 27

if phi =0 force would lead displacement by 90 degrees

Question 28

for froced shm at low frequencies

Answer 28

x tendes to F/k motion is stifness controled

Question 29

for forced shm at high frequancies

Answer 29

x tendes to 0 motion is mass controlled

Question 30

velocity resonce of forced shm occus at

Answer 30

sqrt(k/m)

Question 31

power supplied by driving force. inst

Answer 31

p=Fv=F^2cos(omega t)cos(omega t- phi)/|Z|

Question 32

average power supplied by driving force

Answer 32

F^2cos(phi)/2|Z| cos(phi)=power factor or bF^2/2|Z|^2

Question 33

frequancy at max power dissapated

Answer 33

sqrt(k/m)

Question 34

q value

Answer 34

size of q value tells us the sharpness of the resonave peak Q=omega max/ omega2 - omega 1 =omega max/mb

Question 35

average power supplied by driving force max

Answer 35

F^2/2b