Homework Help: Simple harmomic motion

imy786 · Mar 7, 2007

1. The problem statement, all variables and given/known data

amplitude is kept at 4.0 cm and the vibration
frequency increased to 50 Hz. T
The particle passes through the origin at time t = 0.0 s, travelling in the +y-direction.

(i) At what time does the valve first pass through the position y = 3.0 cm?
(ii) What is the speed at this point?
(iii) What is the acceleration at this point?
(iv) At what positions will the valve have a speed of 6.0ms−1?

2. Relevant equations

w= 2*pi*f
acceleration= -w^2*x
v= rw

3. The attempt at a solution

w= 2*pi*f
= 2*50*pi= 100pi

acceleration= w^2*x
= 100pi*4= 400pi

dont know if this is correct?
also dont know how to get the time and postions part (i and iv)

dimensionless · Mar 7, 2007

What is the equation for the motion?

What do you call the time derivative of the equation of motion?

dobry_den · Mar 7, 2007

imy786 said: ↑

(i) At what time does the valve first pass through the position y = 3.0 cm?
(iv) At what positions will the valve have a speed of 6.0ms−1?

also dont know how to get the time and postions part (i and iv)

ad i) Do you know the equation for simple harmonic motion - i.e. the relation between position and time? Solving this part is just a matter of solving this equation for y = 3.

ad iv) The same story. Just use the equation* for velocity of simple harmonic movement and solve for v = 6 m/s to get the time and use the equation in i) to get the position.

*you might get this one by differentiating the equation in i)

imy786 said: ↑

acceleration= -w^2*x

acceleration= w^2*x
= 100pi*4= 400pi

dont know if this is correct?

don't forget the minus sign - do you know what its significance is?

imy786 · Mar 14, 2007

i)

equation of motion
v2= u2+2as

w= 2pi f
w= 100 pi

equation for SHM:x= asin wt
3= 4 sin 100 pi t
0.75= sin 100pi t
inverse 0.75= 100pi t
48.590...= 100 pi t
t= 1.527 secs

imy786 · Mar 14, 2007

- indicates acceleartion towards the starting position

imy786 · Mar 14, 2007

ii)
v= rw
= 3pi

imy786 · Mar 14, 2007

iv)

a= vw
= 600pi

is questions i- iv correct???

Mentz114 · Mar 14, 2007

i) is correct.
ii) is wrong. To get a velocity differentiate the x=asinwt wrt t.

imy786 · Mar 14, 2007

ii)v= awcos wt

a= 3
w= 100pi
t=0
using this values would this be ok ?
and what about
iii)
iv)

imy786 · Mar 15, 2007

ii)

coz0= 1
v= 300 pi

is this correct?

nithin · Mar 15, 2007

Ok for the first one , you need to form a equation and then solve it . It is given that the y - position is 0 at t=0. w=100pi and A=0.04m (always work with s.i units) . Using these info we can form the equation , y=A Sin(wt) , in this case it would be 0.03=0.04Sin((100pi)(t)) , solving for this will result in the answer!!!

nithin · Mar 15, 2007

Sorry about the double post

nithin · Mar 15, 2007

For part 2 , once again we need to form a equation, this time , we need to form the equation for velocity. Which would be v=-wACos(wt) (it is cos because at origin , y=0) From i) you have your t which you can sustitute into the equation and solve it!!

nithin · Mar 15, 2007

Ok for part 3) , you need to form another equation. The equation would be a=-W^2ASin(wt). Using the ans from part 1) , you can sole the equation and get your ans!!!

nithin · Mar 15, 2007

just for you info imy786 , v=Aw and a= Aw^2 give you the maximum velocity and maximum acceleration.

imy786 · Mar 15, 2007

nithin....

v=-wACos(wt

i dont think it has a minus sign.

book quotes

v= Awcos wt

imy786 · Mar 15, 2007

also

a= Aw^2 sin (wt)
v= Awcos wt

you wrote these equations -

v=-wACos(wt
a=-W^2ASin(wt

imy786 · Mar 15, 2007

URGENT NEED help............

nithin · Mar 15, 2007

imy786 it depends on the situation of the question . Sketch a simple y vs t and v vs t graph side byside ,You will then see whether it is - or +

nithin · Mar 15, 2007

I use cos instead of sin in my equations as my phase angle is 0 as it starts from y=0 at t=0. If u wish u can also use y= A Sin(wt + phi) then v= -AWCos(wt + phi) .Ooops my bad . Sorry .Like i said just draw a graph and you will see what to do.