Examples of Pendulum and Spring Problems Answer KEY

8/9/2019 Examples of Pendulum and Spring Problems Answer KEY

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Examples of

Period Frequency

Problems


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Frequency and Period Problem(Without Period or Frequency given)

Terry Jumps up and down on a

trampoline 30 times in 55 seconds.

What is the frequency with which he

is jumping?

30 times

55 seconds

0.55 Hz


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Frequency and Periodonversion !roblem

Terry Jumps up

and down on a

trampoline witha frequency of

1.5 !. What is

the period ofTerry"s jumping?

".5 Hz

0.#$ sec


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Examples of

Pendulum

Problems


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#ro$lem%

& 't the (alifornia 'cademy of )ciences the

length of the pendulum is%

%0m & '

& The acceleration of gra*ity at this location is%

%. mss & g

& What is the #eriod? *&++++ seconds


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)olution

'ist,' & %0m

g & %. mss

*&++++ seconds

(hoose equation%

)ol*e% +#lug and (hug,

90 m

9.8 m/s/s

9.18 s2

(3.03 s )

(19.0 s )


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- !endulum has a length o 3 m ande/ecutes 0 com!lete vibrations in

$0 seconds.

Find the acceleration o gravity atthe location o the !endulum.

A problem where you

Find the period or frequeny 1st


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- !endulum has a length o 3 m ande/ecutes 0 com!lete vibrations in $0

seconds. Find g.". & cycles seconds

& 0 cycles $0 seconds

& 0.# hz & 0.# sec .

* & " & (" 0.#) seconds & 3.5 seconds

What short cut could - ha*eused?

# vibrations

# seconds is

the time for allthe

oscillations


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' & 3m and *& 3.5 secondsFind the acceleration o gravity at the location

3.5 s & 12(3g)

3.5 s & #. 2(3g)

quare both sides".5 & 3%.43 (3g)

".5 & "".3g

".5(g) & "".3

ivide by ".5

g & %.#5 mss

Heads up!!

If you ÷ by 2π

Use (2π ) !!


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' pro$lem Where

6g6 & %. mss is 7understood89no: you use g&%. mss i,

7g8 not given or as;ed or used %. mss

Part ", - sim!le !endulum has a !eriod o .400

seconds :here 6g6 & %."0 mss. Find the length+

Part , Find 6g6 :here the !eriod o the same!endulum is .4"0 seconds at a dierent location.


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Why are the items green on this pro$lem??

#endulum is not a *aria$le

why is it mar/ed??& - sim!le !endulum has a !eriod o .400

seconds :here 6g6 & %."0 mss. Find the

length+

& Find 6g6 :here the !eriod o the same!endulum is .4"0 seconds at a dierent

location.


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1st find the ength- sim!le !endulum has a !eriod o .400 seconds

:here 6g6 & %."0 mss.

T24 6g7

.002 4 68.9107

.002 38. 68.9107

.008.9107 2

38.

'&".433 m

& Write equation

& )u$stitute :"s

& )quare 4

& ; 38.

'nd < 8.910

& -ns:er :ith

label


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Part ,


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Examples ofSpring

ProblemsHooke’s Law

graphing


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Examples ofusing the graph

to nd the Slopeand the !alue of "k#for springs


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What is the spring

constant for the data

graphed $elow?

Δx(m


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(0=0)

(6,147)

(2,49)

y @ y"

/@/"!lope "

"4$> A 4%>

# m A m

# "

% >

4 m

# "

# " 2$.% &/m'ow do #now the *bel++

*bels on *,es- ise (&) un (m)

!o- rise/run is &/m

Δx(m )


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Examples ofSpring

Problems

$singEquations


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/Hoo;eCs 'a: !roblems

tretch or com!ress A at rest-n anticipation of her first game 'lesia pulls $ac/the handle of a pin$all machine a distance of

5.0 cm. The force constant is 00 >6m. owmuch force must 'lesia eert?

B l H ; C ' bl


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B/am!les o Hoo;eCs 'a: !roblems

List%&x ' ()* cm ' )*( m

k ' +** ,-mFsp'...

-n anticipation of her first game 'lesia pulls $ac/ the handle of a pin$all machine

a distance of 5.0 cm. The force constant is 00 >6m. ow much force must

'lesia eert?

@sp

2 / A

@sp2 00>6m0.05 m7

@sp2 10>

=quation

)u$stitute :"s

'nswer with la$el


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B/am!le o ?scillation s!ringProblems

?scillating or bouncing & Bianca stands on a $athroom scale which

has a spring constant of 0 >6m. Theneedle is $ouncing from side to side.

Bianca"s mass is 190 /g. What is the period

of the *i$rating needle attached to the

spring?

B am!le o ?scillation & Bianca stands on a $athroom scale


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B/am!le o ?scillation!ring

Problem

& Bianca stands on a $athroom scale

which has a spring constant of 0

>6m. The needle is $ouncing from

side to side. Bianca"s mass is 190

/g. What is the period of the

*i$rating needle attached to the

spring?'ist, ; & 0 >m

m & "0 ;g

* & ++

"0 ;g

0>m

0." s

(0.%04 s)

5.$ sec

Spring Problems


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Spring ProblemsUse Both Equations

Example of /ombination of

Hooke’s Law and 0scillation of spring@ind / from oo/e"s aw and then use the

oscillation equation

'utumn a young 0 ;g girl is playing on atrampoline. The trampoline sin/s down % cm whenshe stands in the middle. What is the s!ring

constant+

-f the trampoline then $egins to $ounce :hat :ouldthe requency o the bounces be+

'utumn a young 0 /g girl is playing


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"st Find Force o Dravity on mass

nd Find ; rom Hoo;eCs 'a:

3rd use the oscillation equation toind *

4th convert to Frequency


on a trampoline. The trampoline sin/s

down 8 cm when she stands in the

middle. What is the s!ringconstant+

-f the trampoline then $egins to$ounce :hat :ould the requency

o the bounces be+

'ist , m & 0 ;g

Δx = 9 cm = 0.09m

f =

!he P"#$% Using &oo'e(s "a) an*

+scillation of spring

Fg& m ag

Fs!& ; E/



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'ist , m & 0 ;g

Δx = 9 cm =0.09 m

f =

Using&oo'e(s "a) , +scillation of

spring

"st

Find Force o Dravity on mass

Fg& m ag

Fg& 0;g(@%.mss)

Fg& @ "%# >

ecall

From the FG on the 'ab

F & "%# >?. . .

'utumn a young 0 /g girl is playingExample of ombination of


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'ist , m & 0 ;g

Δx = 9 cm =0.09 m

-s= 9/ $

f=

Example of ombination of&oo'e(s "a) an* +scillation of

spring

nd Find ; rom Hoo;eCs 'a:

Fs!& ; E/

"%# > &;(0.0%m)

"0 >m & ;

'utumn a young 0 /g girl is playing on aExample of ombination of


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'utumn a young 0 /g girl is playing on a

trampoline. The trampoline sin/s down 8 cm

when she stands in the middle. What is the

spring constant?

-f the trampoline then $egins to $ounce :hat

:ould the requency o the bounces be+

'ist , m & 0 ;g

Δx = 9 cm =0.09 m

Fs& "%# >

' = 120 $3m

! =

f =

Example of ombination of&oo'e(s "a) an* +scillation

of spring

3rd use the oscillation equation

to ind *

0 ;g

"0 >m

.00%"$ s

(0.%5 s)

.#0 sec



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trampoline. The trampoline sin/s down 8 cm

when she stands in the middle. What is the

spring constant?

-f the trampoline then $egins to $ounce wh*t

would the frequeny of the bounes be+

'ist , m & 0 ;g

Δx = 9 cm =0.09 m

Fs& "%# >

' = 120 $3m

! = 0./01 sec

f =

Example of ombination of&oo'e(s "a) an* +scillation

of spring

4th convert to requency

.#0 s

".## Hz


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4 part Spring problemCse @g to find the / *alue and then use same

string with same / to find nd mass.-f two +Drumpy Eld Fen, went ice fishing and werecomparing their fish with the etension of the same

spring sol*e the following spring pro$lem% +Drumpy

)am, caught the first fish and magically reali!ed the fishhad a mass of 3 /g. When this fish was suspended on

the spring li/e the one we suspended masses on in la$

the spring stretched so it was 3 cm longer than it was

without the fish. What is the s!ring constant or thes!ring+ +Drumpy Joe, then caught a fish that causedthe same spring to etend 5 cm from the length of the

empty spring. What :as the mass o 7Drum!yIoeCs8 ish+

-f two +Drumpy Eld Fen, went ice

*he Plan to solve,


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Example of 4 part Springproblem

-f two Drumpy Eld Fen went ice

fishing and were comparing their fish

with the etension of the same spring

sol*e the following spring pro$lem%

+Drumpy )am, caught the first fish and

magically reali!ed the fish had a massof 3 /g. When this fish was

suspended on the spring li/e the one

we suspended masses on in la$ the

spring stretched so it was 3 cm longer

than it was without the fish. What is

the s!ring constant or the s!ring?

'ist , m & 3 ;g

Fg& ++

Δx = 5 cm =0.05 m

-sp =

st


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p p p gproblem






magically reali!ed the fish had a massof 3 /g. When this fish was suspended

on the spring li/e the one we

suspended masses on in la$ the spring

stretched so it was 3 cm longer than it

was without the fish. What is the

s!ring constant or the s!ring+

Fg& m ag

Fg& 3;g(@%.mss)

Fg& @ 5 >

'ist , m & 3 ;g

Fg&

Δx = 5 cm = 0.05m

-sp =

@ 5 > & @ Fs

5 > & Fs

st


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p p p gproblem






magically reali!ed the fish had a massof 3 /g. When this fish was suspended

on the spring li/e the one we

suspended masses on in la$ the spring

stretched so it was 3 cm longer than it

was without the fish. What is the

s!ring constant or the s!ring+

'ist , m & 3 ;g

Fg& @ 5 >

Δx = 5 cm = 0.05m

-sp = 116 $

Fs!& ; E/

5 > &;(0.03m)

$500 >m &;

nd use Hoo;e to ind the ; value


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xamp es o par pr ng rumpy oe4s5 Fish


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p p p gproblem

py

&67 F6

&67 :A!!

-JB PK>DLL

+Drumpy Joe, then caught a fish thatcaused the same spring to etend 5 cm

from the length of the empty spring.

What :as the mass o 7Drum!yIoeCs8 ish+

'ist , m & +++ ;g

Fg& @3$5 >

Δx = 6 cm = 0.06m

-sp = 576 $

' = 7600 $3m

4th convert :eight to mass

Fg& m ag

@3$5 >& m(@%.mss)

m& 3.3 ;g

@ 3$5 > & @ Fs

3$5 > & Fs

E ti


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Equation

Sheet

Sli*esfor

Springsan*

Pen*ulums

#eriod and @requency notes


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#eriod and @requencyGnotes& ert! is unit that means 16sec

& '$$re*iated GGGGGGG !

& Fega ert! H@F radio

& Iilo ert! H 'F radio;*


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#eriod and @requency& ert! is unit that means 16sec

& '$$re*iated GGGGGGG !

& Fega ert! H@F radio

& Iilo ert! H 'F radio

@se when you

#now

either or f

;*


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Escillations for #endulums onlyG>otesength of the pendulum and gra*ity determine how fast

the pendulum oscillates $ac/ and forth.;*


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;*


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!age 4 !ace M3

)prings only

#eriod and @requency


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#eriod and @requency& ert! is unit that means 16sec !7


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oo/e"s aw for )prings only


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)prings only

Examples of Pendulum and Spring Problems Answer KEY

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