simple harmonic motion

Question 1

conditions for simple harmonic motion

Answer 1

-acceleration is proportional to displacement

-must act towards equlibrium

extra information
- force is proportional to objects displacement
-acceleration is in opposite direction to displacement

Question 2

defining equation for SHM

Answer 2

F = - constant x displacement
F=-k * x

Question 3

examples of SMH

Answer 3

-a mass suspended on a spring
-end of a vibrating tuning fork
-a cork bobbing up and down on a wave

Question 4

what is frequency in SHM

Answer 4

number of full cycles that occur each second

Question 5

what is a full cycle in SHM?

Answer 5

A full cycle is the motion from maximum positive displacement, to maximum negative
displacement and then back to the maximum positive displacement again

Question 6

what is time period in SHM

Answer 6

The time period is the length of time it takes to complete a cycle

Question 7

SHM oscillations are periodic, what does this mean?

Answer 7

meaning they are repeated in regular intervals according to their frequency or time period

Question 8

why does an object in SHM have a restoring force

Answer 8

to return it to its equilibrium position

Question 9

what is the restoring force

Answer 9

This restoring force will be directly proportional, but in the opposite direction, to the displacement of the object from the equilibrium position

restoring force acts in same direction as acceleration

Question 10

explain why a person jumping on a trampoline is not an example of simple harmonic motion

Answer 10

-The restoring force on the person is not proportional to their distance from the equilibrium position
-When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
-This does not change, even if they jump higher

Question 11

equation for acceleration

Answer 11

a = −⍵2x

a = acceleration
⍵ = angular frequency (rad s-1)
x = displacement (m

Question 12

what does the a = −⍵2x show

Answer 12

The acceleration reaches its maximum value when the displacement is at a maximum ie. x = A (amplitude)

The minus sign shows that when the object is displaced to the right, the direction of the acceleration is to the left and vice versa (a and x are always in opposite directions to each other)

Question 13

what are the key features of an acceleration displacement graph

Answer 13

The gradient is equal to −⍵2
The maximum and minimum displacement x values are the amplitudes −A and +A

Question 14

when do we use x = A cos (⍵t)

Answer 14

This equation can be used to find the position of an object in SHM with a particular angular frequency and amplitude at a moment in time

A is amplitude
t is time

Question 15

when does the x = A cos (⍵t) occur

Answer 15

An object is oscillating from its amplitude position (x = A or x = −A at t = 0)

The displacement will be at its maximum when cos(⍵t) equals 1 or −1, when x = A

Question 16

what equation for displacement can we use when the object is oscillating from equilibrium position(x = 0 at t = 0)

Answer 16

x = A sin (⍵t)

Question 17

how can you calculate the maximum acceleration using w and A

Answer 17

max accleration = w^2 A

Question 18

small angle approximation for sin x

Answer 18

sin x = x

Question 19

small angle approximation for cos x

Answer 19

cos x = 1 - x^2/2

Question 20

what are free vibrations

Answer 20

the frequency a system tends to vibrate at in a free vibration is called the natural frequency

Question 21

define forced vibrations

Answer 21

a driving force causes the system to vibrate at a different frequency

Question 22

forced vibrations at higher driving frequencies

Answer 22

the phase difference between the driver and the oscillations rises to pi radians

Question 23

forced vibrations at lower frequencies

Answer 23

oscillations are in phase with the driving force

Question 24

what will happen when resonance occurs

Answer 24

when resonance occurs, that’s when it will most efficiently transfer energy to the system, the phase difference will be pi/2 radians

Question 25

what is damping

Answer 25

damping occurs when an opposing force dissipates energy to the surroundings

Question 26

what is critical damping

Answer 26

reduces the amplitude to zero in the quickest time

Question 27

what is overdamping

Answer 27

when the damping force is too strong and it returns to equilibrium position slowly without oscillation

Question 28

what is underdamping?

Answer 28

when damping force is too weak and it oscillates with exponentially decreasing amplitude

Question 29

what happens to a vibration with greater damping

Answer 29

greater damping the amplitude is lower at all frequencies due to greater energy losses from the system

resonant peak is also broader because of damping