Working out experimental periodic time from a wieghted spring in s.h.m

[shaun_598]

Homework Statement

A spring hanging from a lab stand has an equilibrium position of 66mm.
Weights are added in 50g increments from 100g upto 250g, record the spring displacement and work out the spring constant.

Part 2:
With each mass in turn pull them down 20mm from their equilibrium point and record the avergae time taken to complete 20 oscillations. Plot the reults of mass against experimental periodic time and also against periodic time squared.

Homework Equations

For spring constant : k=mg/x
Where m= mass, g= gravity, x= spring displacement

For periodic time: T = 2p √m/k

The Attempt at a Solution

The first part I am sure I've done correctly,

Number Mass (kg) Spring displacement (m) Spring constant (N/m)
1 0.05 0 n/a
2 0.1 0.0195 50.31
3 0.15 0.039 37.73
4 0.2 0.061 32.16
5 0.25 0.081 30.28

Im struggling with working out periodic time. The equation I've been given has 2p in it. What is p representing?

Any help on this will be very appreciated as its driving me mad.
thanks

 

[tiny-tim]

welcome to pf!

hi shaun_598! welcome to pf!

For periodic time: T = 2p √m/k
…
The equation I've been given has 2p in it. What is p representing?

π (pi)

(2π ≈ 360°)

 

[shaun_598]

hi shaun_598! welcome to pf! π (pi)

(2π ≈ 360°)

Thank you, that a massive help

So T = 2π x √m/k

So using table in the question
100g mass and 50.31N/m constant

T= 2π x √0.1/50.31
= 0.28 (Not sure what units this should be? Seconds?)

Have i done this correctly?

thanks

 

[tiny-tim]

yup, looks fine!

(and N/m is an SI measurement, so so long as everything else is also SI, the result will be too, so yes, it's in seconds )

 

[shaun_598]

yup, looks fine!

(and N/m is an SI measurement, so so long as everything else is also SI, the result will be too, so yes, it's in seconds )

Thank you very much

 

[shaun_598]

What I've worked out here is theoretical periodic time?

Im also asked to work out experimental periodic time.
Take the 100g mass. It took an average of 8.5 seconds to complete 20 oscillations.
One oscialltion is a complete up and down so as i undertsand it this is one period.
So is this just as simple as 8.5/20

 

[tiny-tim]

One oscialltion is a complete up and down so as i undertsand it this is one period.
So is this just as simple as 8.5/20

by "up and down" do you mean "up and down left and up and down right" (one complete cycle)?

if so, yes 8.5/20 s ​

 

[shaun_598]

by "up and down" do you mean "up and down left and up and down right" (one complete cycle)?

if so, yes 8.5/20 s ​

I mean if you pull on the spring and start when its at the bottom of its travel, wait for it to got to extent of of its travel the oppoisite way and come back to its bottom travel. Thats what we said was one oscialltion.

 

[MrWarlock616]

Why is the spring constant not a constant value in your table as expected?

 

[tiny-tim]

I mean if you pull on the spring and start when its at the bottom of its travel, wait for it to got to extent of of its travel the oppoisite way and come back to its bottom travel. Thats what we said was one oscialltion.

oh yes, that's right

(i was thinking it was a pendulum )

 

[shaun_598]

Why is the spring constant not a constant value in your table as expected?

Im not sure about that yet, I am looking into it. Its what the content of my report will be focused on.
Anyone have any ideas?