Angular frequency.Watch

Announcements
Thread starter 6 years ago
#1
This question is in relation to Hookes law and angular frequency (I think).

Q. Use the principle of dimensional homogeniety to deduce an expression for the frequency of oscillation in terms of stiffness (k), the mass (m) and the gravitational cosntant (g).

My answer is: fosc= .

Is this right?

Sorry I do elec eng so I don't do this kind of physics very often but there's going to be something similar in one of my exams tomorrow, so any help would be great. Cheers 0
6 years ago
#2
(Original post by 3 Phase Duck)
This question is in relation to Hookes law and angular frequency (I think).

Q. Use the principle of dimensional homogeniety to deduce an expression for the frequency of oscillation in terms of stiffness (k), the mass (m) and the gravitational cosntant (g).

My answer is: fosc= .

Is this right?

Sorry I do elec eng so I don't do this kind of physics very often but there's going to be something similar in one of my exams tomorrow, so any help would be great. Cheers How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
0
Thread starter 6 years ago
#3
(Original post by Stonebridge)
How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
Ahh right, ok. I'll give it a shot.
0
Thread starter 6 years ago
#4
(Original post by Stonebridge)
How did you work out that answer?

The way to do these is to set up the right of the equation so it has the same units (dimensions) as the left. This means equating the mass (kg), length (m) and time (s) units on both sides.

On the left you have frequency which is seconds-1 (unit) or time-1 (dimension)
On the rhs you have the spring constant, g, and mass
You know the units of k and g (m is just mass)
Can you take it from there.
Ok so would it just be fosc= 0
6 years ago
#5
Mg has units of force, and k force per metre....
0
Thread starter 6 years ago
#6
(Original post by Pythononian)
Mg has units of force, and k force per metre....
Tbh I'm unsure where g comes into it really.
0
Thread starter 6 years ago
#7
I'm confused here. mg (as in small g, the acceleration due to gravity) = -kx.

and But where does the gravitational constant come into it?
0
6 years ago
#8
On the rhs we have
mass - kg
g - ms-2
k - force per metre = Nm-1 and N = kgms-2 from F=ma
so Nm-1 is kgms-2m-1

assume on the rhs the terms are [m]a[g]b[k]c
so on the rhs we have
[kg]a[ms-2]b[kgs-2]c
on the left we have
s-1

Find the values of a b and c that balance the equation so that there is s-1 on both sides
0
Thread starter 6 years ago
#9
(Original post by Stonebridge)
On the rhs we have
mass - kg
g - ms-2
k - force per metre = Nm-1 and N = kgms-2 from F=ma
so Nm-1 is kgms-2m-1

assume on the rhs the terms are [m]a[g]b[k]c
so on the rhs we have
[kg]a[ms-2]b[kgs-2]c
on the left we have
s-1

Find the values of a b and c that balance the equation so that there is s-1 on both sides
Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?
0
6 years ago
#10
(Original post by 3 Phase Duck)
Ok I'm starting to feel really stupid now, but would it be a=-1, b=3, c=3?
No,because, for a start, b must be zero.
I can see that you haven't done an example of (or been taught?) dimensional analysis. It's a bit difficult to teach you it here from scratch.
This is how it's done. I suggest you find some notes on this (Google it) and study them.

We have
f = magbkc balancing for m gives b=0 as there is no m term on the left

looking at kg gives
0 = a + c -------(1)

looking at s gives
-1 = -2b -2c
which gives
-1 = -2c as b=0
So
c = ½

and subbing back in (1)
a = -½

This gives the formula as 0
Thread starter 6 years ago
#11
(Original post by Stonebridge)
No,because, for a start, b must be zero.
I can see that you haven't done an example of (or been taught?) dimensional analysis. It's a bit difficult to teach you it here from scratch.
This is how it's done. I suggest you find some notes on this (Google it) and study them.

We have
f = magbkc balancing for m gives b=0 as there is no m term on the left

looking at kg gives
0 = a + c -------(1)

looking at s gives
-1 = -2b -2c
which gives
-1 = -2c as b=0
So
c = ½

and subbing back in (1)
a = -½

This gives the formula as Cheers, we haven't been taught because we are supposed to know this already. However I've never done A-level physics so this is quite new to me.

Thanks anyway, it actually makes more sense when you explain it like that. I was getting confused because of b and where G lies in all of this.
0
X

new posts Back
to top
Latest
My Feed

Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

University open days

• University of East Anglia
Sun, 20 Oct '19
• University for the Creative Arts
Sun, 20 Oct '19
• University of Gloucestershire
Sun, 20 Oct '19

Poll

Join the discussion

Have you made up your mind on your five uni choices?

Yes I know where I'm applying (65)
65.66%
No I haven't decided yet (21)
21.21%
Yes but I might change my mind (13)
13.13%