oscillations

Question 1

define displacement

Answer 1

the distance from the equilibrium position in a given direction
m

Question 2

define frequency

Answer 2

number of oscillations per unit time Hz

Question 3

define period

Answer 3

time taken for one complete oscillation
s

Question 4

define amplitude

Answer 4

the maximum displacement form the equilibrium position

Question 5

define simple harmonic motion

Answer 5

the specific type of oscillation when the acceleration is directly proportional to the displacement from a fixed position in the opposite direction

Question 6

list 5 characteristics of SHM

Answer 6

1. the oscillation is periodic
2. there is a central equilibrium position called fixed position
3. the restoring force is always towards the fixed postion
4. restoring force is proportional to displacement
5. The object’s displacement, velocity and acceleration change continuously

Question 7

what is the relationship of SHM

Answer 7

acceleration is directly proportional to the negative displacement;
where the negative indicates opposite direction

Question 8

relation frequency and period

Answer 8

f = 1/T

Question 9

relation angular frequency (velocity) with T

Answer 9

ω = 2π/T = 2π*f

Question 10

equation of x displacement in respect of time

Answer 10

1. x = x0 * sin(ωt), start from equilibrium moving positive
2. x = - x0 * sin(ωt), start from equilibrium moving negative
3. x = x0 * cos(ωt), start from maximum

4.. x = - x0 * cos(ωt), start from minimum

Question 11

equation of v, velocity in respect of time

Answer 11

v = d/dt (x0* sin (ωt)), differentiate of equation of displacement

= x0ωcos(ωt)

Question 12

what is equation of maximum velocity

Answer 12

v max = ω * x0

Question 13

equation of v in respect of displacement

Answer 13

v = +- ω * √(x0^2- x^2)

Question 14

equation of acceleration

Answer 14

a = - x0 * ω^2 sin(ωt)
a = - ω^2 * x
differentiate of equation of velocity

Question 15

equation of max acceleration

Answer 15

a = - ω^2 * x0

Question 16

describe the interchange between kinetic and potential energy during simple harmonic motion

Answer 16

as kinetic energy increase potential energy decreases, they add up to constant. E (should know the graph form notes)

Question 17

equation of Er, total energy (oscillation)

Answer 17

E = 1/2 * m * ω^2 * x0^2

Question 18

define damping

Answer 18

The reduction of amplitude of oscillations due to resistive forces on the oscillating system causing lose of energy to the surrounding

Question 19

does frequency change due to damping

Answer 19

no

Question 20

what are the three types of damping

Answer 20

1. light
2. heavy
3. critical

Question 21

what does the graph of light damping look like

Answer 21

exponential decay, light damping has oscillations, with smaller amplitude each cycle until 0

Question 22

graph of heavy damping

Answer 22

there is no oscillation, the amplitude slowly turns zero

Question 23

critical damping

Answer 23

there is no oscillation, amplitude returns to zero within the shortest time possible

Question 24

what is natural frequency

Answer 24

frequency when object is allowed to oscillate freely (without any resistive force such as friction)

Question 24

what is resonance

Answer 24

maximum amplitude of oscillation that occurs when an oscillating system is forced to oscillate at its natural frequency

Question 24

how is the amplitude frequency graph look like with forced frequency and natural frequency are the same

Answer 24

the amplitude reaches max when the forced and natural frequency is the same (reach resonance), the amplitude decreases as their difference increase (either forced frequency increase or decrease)

Question 25

equation for Ek (oscillation)

Answer 25

Ek = 1/2 * m * ω^2 * (x0 - x)^2 = Er - Ep

Question 26

equation for Ep (oscillating)

Answer 26

Ep = E = 1/2 * m * ω^2 * x^2

Question 27

examples of simple harmonic motion

Answer 27

guitar string; mass on spring