oscillations

Question 1

simple harmonic motion

Answer 1

experiences a restoring force acting towards the centre of equilibrium. this force is directly proportion to the objects distance from the equilibrium
F=-kx

Question 2

what provides the restoring force on a pendulum

Answer 2

the horizontal component of gravity

Question 3

acceleration of the bob

Answer 3

is directly proportional to the displacement and is in the opposite direction
a=-xw^2

Question 4

angular speed (w)

Answer 4

the angle an object moves through per unit time

Question 5

how are displacement-time and velocity-time graphs related

Answer 5

velocity-time is the differential of displacement-time.

Question 6

time period

Answer 6

pendulum: 2 πrootl/g
spring: 2 πrootm/k

Question 7

resonance

Answer 7

where the amplitude of oscillations of a system drastically increases due to gaining an increased amount of energy from the driving force (maximum amount of energy). occurs we the driving frequency is equal to the natural frequency

Question 8

damping

Answer 8

resonance can be damaging to structures, damping can be used to decrease the effects of resonance. damping is where a force acts on an oscillating system and energy is lost from the system to its environment, leading to a reduced amplitude of oscillations.

Question 9

energy conservation in SHM

Answer 9

an oscillating system cannot gain or lose energy unless there are external forces acting on it, this is the principle of conservation of energy. For any SHM system, Ek is transferred to Ep and back as the system oscillates

Question 10

where is kinetic and potential energy maximum during SHM

Answer 10

potential energy is max at the max amplitude of oscillations. kinetic energy will be max at the point of equilibrium.
in an undamped system, the total amount if energy in the system remains constant

Question 11

free vibrations

Answer 11

occur when no external force is continuously acting on the system, therefore the system oscillates at natural frequency

Question 12

forced vibrations

Answer 12

system experiences an external driving force which causes it to oscillate, the frequency of this driving force, known as the driving frequency

Question 13

critical damping

Answer 13

reduces amplitude to zero in the shortest possible time

Question 13

light damping

Answer 13

where the amplitude gradually decreases by a small amount each oscillation

Question 14

heavy damping

Answer 14

the amplitude reduces slower than with critical damping, but also without an additional oscillations (overdamping)

Question 15

damping and frequency

Answer 15

as the degree of damping increases, the resonant frequency decreases, the max amplitude decreases and the peak of the max amplitude gets wider

Question 16

ductile material damping

Answer 16

a ductile material is one which can undergo a large amount of plastic deformation before fracturing, meaning it will be permanently deformed. the plastic deformation of a ductile material can be used to reduce the amplitude of oscillations, this happens because energy us used to deform the material, decreasing the kinetic energy of the system and so the amplitude of oscillations decreases

Question 17

maximum acceleration during SHM

Answer 17

occurs at the max amplitude, so as a=w^2x, the max acceleration is a+w^2A

Question 18

maximum velocity during SHM

Answer 18

v=wrootA^2-x
as it is greatest at equilibrium x=0 and so v=wA or v=2πfA

Question 19

how can max vertical height of a pendulum be used

Answer 19

equate to GPE to convert into kinetic energy and so vmax

Question 20

why is the SHM equation an approximation

Answer 20

it assumes the motion is in a straight line, therefore a small angle must be used when counting ten oscillations and dividing by ten, in order for your answer to be applicable

Question 21

how much energy is left after damping?

Answer 21

energy is proportional to v^2 which is proportional to A^2, therefore if the amplitude is halved, the total energy has been quartered