Week 2 Damped Harmonic Motion

Question 1

what is a damping force

Answer 1

force that opposes SHM causing energy to dissipate leading to a stop in oscillations

Question 2

what is often true of damping (give the damping force equation)

Answer 2

damping is often due to frictional forces that are proportional to velocity
F = -bv
b is the damping constant

Question 3

what is the damped equation of motion

Answer 3

a + γv + ω0^2x = 0
where ω0 is resonant frequency
γ is b/m

Question 4

give a brief and general description for motion for light damping. heavy damping and critical damping

Answer 4

light - the oscillator will retain the oscillating behaviour with a decaying amplitude
heavy - oscillations are supressed
critical - system returns to eqm in shortest time without oscillating

Question 5

what is the frequency condition for the different types of damping

Answer 5

ω0^2 > γ^2/4
ω0^2 < γ^2/4
ω0^2 = γ^2/4

Question 6

define relaxation time and its equation

Answer 6

it is the time required for the energy to drop to 1/e of its initial value
relaxation time = γ^-1

Question 7

define the quality factor and give its general equation

Answer 7

dimensionless characteristic that indicates how quickly an oscillator returns to rest
Q = ω0 / γ

Question 8

give the fractional energy change per cycle, fractional energy changer per radian equations

Answer 8

fractional energy change per cycle = 2π/Q

fractional energy change per radian = 1/Q

Question 9

give the energy related definition of Q

Answer 9

Q is the energy stored in the oscillator to the energy dissipated per radian