chapter 17 - oscillations

Question 1

what is formula for angular frequency , w ?

Answer 1

2 pi / T or 2 pi X frequency

Question 2

define simple harmonic motion?

Answer 2

the acceleration is directly proportional to its displacement and acceleration acts opposite direction to displacement

Question 3

what is formula for simple harmonic motion ?

Answer 3

a is proportional to -x

Question 4

what does the graph of acceleration against displacement look like?

Answer 4

downward sloping through the origin

Question 5

equation for velocity in simple harmonic motion?

Answer 5

v= w ( square root ( Amplitude^2 - displacement^2))

Question 6

equation for maximum velocity?

Answer 6

v= w X Amplitude

Question 7

what are the equations for displacement in simple harmonic motion?

Answer 7

x = A sin (w X t) or x = A cos (w X t)

use cosine when amplitude is at max at start

Question 8

what is the phase difference of two pendulums when one is at max positive displacement and the other is at max negative displacement?

Answer 8

antiphase, phase difference of pi radians

Question 9

what is the phase difference of two pendulums when both are at max positive displacement?

Answer 9

in phase , phase difference = 0

Question 10

what is an isochronous oscillator?

Answer 10

it means that as amplitude increases time period remains the same, this is due to speed also increasing.

Question 11

what are the two stores of energy in a simple harmonic motion?

Answer 11

the 2 stores are kinetic energy and potential energy (gravitational or elastic) with the sum at each displacement always equaling the total energy

Question 12

formula for kinetic energy in simple harmonic motion?

Answer 12

1/2 X k (A^2 - x^2) where k is the force constant

Question 13

what does the graph energy against displacement look like?

Answer 13

it is one U shaped curve with another inverted U curve on top with the peak of curves touching the total energy and 0 energy, they cross at exactly half total energy.

Question 14

what is damping?

Answer 14

damping is when an external force acts on an oscillator reducing the amplitude of its oscillations.

Question 15

when is damping used?

Answer 15

in bike suspension to absorb energy but maintain control.

Question 16

what are the 3 forms of damping and give examples with pendulum?

Answer 16

light- pendulum oscillating in air
heavy - pendulum oscillating in water
very heavy - pendulum oscillating in thick oil

Question 17

what is free oscillations and what is the frequency called?

Answer 17

free oscillations are when a mechanical system is displaced from its equilibrium position then allowed to oscillate without external forces. its frequency is the natural frequency.

Question 18

what is forced oscillations and what is the frequency called?

Answer 18

this is when a periodic driver force is applied to an oscillator. the frequency is called the driving frequency.

Question 19

what occurs when the driving frequency is equal to natural frequency?

Answer 19

the object will resonate, this results in dramatic increase of amplitude and if not damped the system will break

Question 20

what is exponential decay?

Answer 20

exponential decay is when damping decrease amplitude by the same factor in equal time intervals.

Question 21

what are uses of resonance?

Answer 21

• keep time in clocks using resonance of pendulum

- MRI scans

Question 22

as amount of damping increase what occurs?

Answer 22

• amplitude decreases
• maximum amplitude occurs at lower frequency then natural frequency
• peak on graph of amplitude against frequency become flatter and broader.

Question 23

For an object moving with SHM, what is the equilibrium position?

Answer 23

The midpoint of its motion

Question 24

What is the displacement, x, of an object moving with SHM?

Answer 24

The distance and direction from the equilibrium position

Question 25

What is the amplitude, A, of an object moving with SHM?

Answer 25

The maximum displacement from the equilibrium position