Simple Harmonic Motion

Question 1

Periodic Motion

Answer 1

a motion which repeats after a finite amount of time

Question 2

equation that proves when a motion is periodic??

Answer 2

x (t + T) = x(t)

same with v instead of x (velocity vs position)
if T is time period and t is actual time spent, means will return to same position and velocity regularly/PERIODICALLY!! <3

Question 3

oscillation

Answer 3

complete back and forth

Question 4

frequency!! freak quency

Answer 4

oscillations per time period, given by

f = 1/T

measured in s ^-1 or Hz, 1 Hz = one oscillation /second

Question 5

T

Answer 5

period/time to complete one oscillation

Question 6

general notes on sin function

Answer 6

begins at origin, 0

period of 2pi unless changed

amplitude of 1 unless changed

up first

o with line through it would be 3pi/4

Question 7

general nots on cosine

Answer 7

begins at y = 1

period of 2pi unless changed

amplitude of 1 unless changed

down first

o with line through it would be 0

Question 8

manipulation of cosine and sin

Answer 8

[A] cos/sin(x) - og amplitude would be one, this is multiplied by A, if A> 1 stretch, <1 compression. If A is negative, graph is flipped along the x axis!

cos/sin ([n] x) - horizontal stretch/compression, og wavelength is 2pi, if any number before x etc, divide 2pi by that to get new wavelength!! ex. sin (2x), 2pi/2 = pi therefore new wavelength is pi. IF n is -, technically flip over the y axis but same results as flip over x

cos/sin (x +/- g) - shift left or right by g units, COUNTERINTUITIV`E if (x +…) shift to the left! if (x - ….) shift to the right

cos/sin (x) + h - shift whole ass graph up or down by h! actually makes sense, + h shift up so midpoint is 0 + h, if - h shift down so midpoint is 0 - h

Question 9

relationship between sin and cos, how to transform into the other

Answer 9

sin (theta + pi/2) = cos(theta)

cos (theta - pi/2) = sin (theta)

Question 10

what the heck does multivalued mean???

Answer 10

multiple values of theta/ angle inserted into sin/cos equation will give the same results

Question 11

IMPORTANT equation for simple harmonic motion!!!

Answer 11

x(t) = A cos (wt + [o with line down center])

A = amplitude

w = angular frequency (calculated by 2pif or 2pi/T) f is frequency i think confirm this

[o with line down middle] = phase constant (determined by initial position and velocity of graph, related to position on the unit circle

Question 12

how to calculate fancy w???

Answer 12

2pi/T OR 2pif where T is the period and f is frequency because remember frequency = 1/T

units = radians

Question 13

how to determine phase constant

Answer 13

fancy o with line (phase constant) = cos^-1 ([x(0)] / A)

x(0) is y position at x = 0

Question 14

how to find velocity of shm

Answer 14

take the derivative of position function!!!

v(t) = dx(t)/d(t) = d/dt (Acos (wt + funky circle)

v(t) = -(wA) sin (wt + funky circle)

Question 15

calculate max velocity???

Answer 15

vmax = wA OR (2pi/T x A)

Question 16

derivative of cosx

Answer 16

-sinx! if Acos(wt + h)

derivative is -(Aw) sin (wt + h)

Question 17

derivative of sinx

Answer 17

cosx!!!

Question 18

what is velocity when max displacement???

Answer 18

0!!

Question 19

what is displacement when velocity max?

Answer 19

ZERO

Question 20

how do you find acceleration?

Answer 20

derivative of velocity equation!

d/dt (-wA sin (wt + funky circle))

= -(w^2 * A) cos (wt + funky circle!)

Question 21

how do you calculate maximum acceleration??

Answer 21

w^2 * A

Question 22

relationship between acceleration and displacement

Answer 22

always exactly opposite, literally just flip the graph (with different ampitudes)

Question 23

relationship between acceleration and velocity

Answer 23

when the slope of velocity is positive (ex moving from -A to +A), graph of acceleration is positive

when slop velocity negative (+A to -A), graph of acceleration is negative

Question 24

relationship between force and SHM

Answer 24

if direction of force is always opposite to direction of the displacment the motion will be simple harmonic motion

Question 25

equation for F(t)

Answer 25

= -(mw^2) * x(t)

x(t) is formula for displacement

Question 26

hooke’s law of force

Answer 26

F = -k x

k is spring constant

Question 27

k calculation

Answer 27

spring constant. = m w^2

Question 28

relationship w and k

Answer 28

w = √k/m

Question 29

how to determine the length a spring is stretch when you add a weight (vertical mass-spring)

Answer 29

if spring originally at length L, string stretches by d

d = mg / k

Question 30

IMPORTANT relationship between w and d

Answer 30

w = √g/d

Question 31

what is w???

Answer 31

angular frequency

Question 32

relationship between spring constant and frequency

Answer 32

higher spring constant = higher frequency because angular freqency = √(spring constant/mass)

Question 33

relationship between mass and frequence

Answer 33

as mass gets greater, frequency smaller