# What frequency of vibration is required?

## Homework Statement

(a) acceleration amplitude of 100 ms−2 with a vibration amplitude of 5.0 cm.

(i) What frequency of vibration is required?
(ii) What is the maximum speed ?
(iii)What is the time delay between the points of maximum acceleration and
of maximum speed?

## Homework Equations

speed= f * wavelength

f= 1/ time period

## The Attempt at a Solution

(i)

a= -2*pi*f*x

100= -2*pi*f*0.05

400=-pi *f

400/ -3.141= f

f= - 127.32 Hz

(can frequency be minus)??

(ii)

speed = integral of accelration
a= -2*pi*f*x

speed= f * wavelength

(iii)

time delay
f= 1/ time period
t= 1/ - 127.32 Hz
t= 0.00785423

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Seems to me like this is a problem in simple harmonic motion. The acceleration to be found is the acceleration of a point on the medium that the wave is travelling through. As a wave travels through a medium it causes the particles within that medium to oscillate, each one about their own equilibrium position.
Smple harmonic motion is the simplest form of oscillation. Its defining equation is:-

a= -2*pi*f*x

where
a = acceleration
f= frequency
x= displacement from equilibrium position (max value = amplitude)

Hope this gets you started.

a= -2*pi*f*x

100= -2*pi*f*0.05

400=-pi *f

400/ -3.141= f

f= - 127.32 Hz

(can frequency be minus)??

(ii)

speed = integral of accelration
a= -2*pi*f*x

speed= f * wavelength

f= - 127.32 Hz

(iii)

time delay
f= 1/ time period
t= 1/ - 127.32 Hz
t= 0.00785423

is this correct (i, ii, iii)

well is this correct???

hage567
Homework Helper
"a= -2*pi*f*x"

This is not an equation for acceleration. Check the units, they don't work out. Maybe you didn't copy it from your book correctly? Go look it up again.

well is this correct???
Please try to be patient about waiting for replies. Last edited:
(a) acceleration amplitude of 100 ms−2 with a vibration amplitude of 5.0 cm.
(i) What frequency of vibration is required?

a= -2*pi*f*x

i have used it....doesnt work..??

a= -2*pi*f*x

where
a = acceleration
f= frequency
x= displacement from equilibrium position (max value = amplitude)

Hope this gets you started.
--------------------------------------------------------

a= -2*pi*f*x
100=-2*3.141*0.05* f
f= 317 Hz...

is this correct...using the formula u gave

hage567
Homework Helper
a= -2*pi*f*x

where
a = acceleration
f= frequency
x= displacement from equilibrium position (max value = amplitude)

Hope this gets you started.
--------------------------------------------------------

a= -2*pi*f*x
100=-2*3.141*0.05* f
f= 317 Hz...

is this correct...using the formula u gave
I'm not the one that gave you the formula. You started off with it yourself by the looks of things. But it doesn't matter, it is still wrong.
Look at it carefully. The units work out to those of velocity, not acceleration. Check it. So, what would the right equation be? It's very similar.

sorry HAGE,

apeeling gave me the INCORRECT acceleration formula,

well if the formula is velocity then u differtiate to get accelration.

But i dont want to start off with INCORECT formula.

-------------------------------------------------------------

w= 2*pi*f

accelration= -W^2 x

100= -w^2 * 0.05
2000= -W^2
+- square root of 2000= w

w=2*pi*f

+- square root of 2000= 2*pi*f

+- square root of 2000/2*pi= f

---------------------------------------

hage567
Homework Helper
"accelration= -W^2 x"

Get rid of the negative sign, I don't understand why it's there. Do that, and you have the right equation.

formula booklet states a minus sign.

Does that depend where u take the point of refrence?

so doing this kind of problem you leave minus sign. What is the signifcan of minus sign again.

-----------------------------------------------------------------

(ii) What is the maximum speed ?
a= v w
100= v w

would that be correct method

---------------------------------------
(iii)What is the time delay between the points of maximum acceleration and
of maximum speed?

what formula needed to work at time delay

hage567
Homework Helper
formula booklet states a minus sign.
Does that depend where u take the point of refrence?

so doing this kind of problem you leave minus sign. What is the signifcan of minus sign again.

-----------------------------------------------------------------

(ii) What is the maximum speed ?
a= v w
100= v w

would that be correct method

---------------------------------------
(iii)What is the time delay between the points of maximum acceleration and
of maximum speed?

what formula needed to work at time delay
For the maximum acceleration I would think it would be positive. But whatever, go by what you think.
(b): Yeah, i guess that works. You could also use the equation for speed that you were using by accident for acceleration.
(iii): Have you tried to come up with it yourself?

(iii)
x= Asin (wt)

v= Awcos (wt)
100/w= v

100= Aw^2 (wt)

A is a constant, what will this constant be?

would this be right equation for (iii)

hage567
Homework Helper
I don't understand what you're trying to show. What will what constant be? You can reason this out as well, without any math. So if you can get both to agree then you probably have it right.

Do watch out for the signs in this, you just have to be careful what case you are taking (like at max acceleration, or just at some point x that is not at max acceleration). Sorry I know that isn't very clear, but I think you're aware of it anyway.

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well is was that the corect formual to work out time delay.

i quoted the formula...from formula booklet

need help on this question??

i)
w= 2 pi f

accerleation= A w^2
100 = 0.05 * w^2
w= 44.721

44.721= 2 pi f
f= 7.11 Hz

ii)
V= Aw
= 0.05* 44.721
=2.23 m/s

is this corect?

urgent help required is this CORRECT???

hage567
Homework Helper
i)
w= 2 pi f

accerleation= A w^2
100 = 0.05 * w^2
w= 44.721

44.721= 2 pi f
f= 7.11 Hz

ii)
V= Aw
= 0.05* 44.721
=2.23 m/s

is this corect?
I would say those are correct.

(iii)
x= Asin (wt)

v= Awcos (wt)
100/w= v

100= Aw^2 (wt)

is this correct method

hage567
Homework Helper
(iii)
x= Asin (wt)

v= Awcos (wt)
100/w= v

100= Aw^2 (wt)

is this correct method
You keep quoting this formula from your formula booklet. Can you explain what you are doing with it? How are you getting the time difference out of this? Work it out completely, so I can see what you're doing.

What you are looking for is the time difference between when the maximum velocity is reached and when the maximum acceleration is reached. So, you need to figure out the relationship between the two. Try drawing out the x(t), v(t) and a(t) functions to see the this. Once you see what the phase is between them (how they are shifted with respect to one another), you can figure out the time difference because you know the frequency (and therefore the period) of the motion.

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x= Asin (wt)
v= Awcost sin (wt)
aceleration=-Aw^2 sin wt

phase differnce between them would be of 90 degrees (the differnce between sin and cos)

still need more help to do quesiton (iii)

(iii)What is the time delay between the points of maximum acceleration and
of maximum speed?

hage567
Homework Helper
OK, so you know the phase difference. How much of a wavelength does 90 degrees represent? So, how much time has passed in 90 degrees (keep in mind you know the period, so you already know how much time it takes for one full wavelength). Figure that out and you have your answer.