Solving Equations: Finding k and a with t=2π√(m/k) and s=ut+½at²

[Large dwarf]

Homework Statement

t=2π (square root m/k). Find the value of 'k'.

2. The attempt at a solution

t2= 4π^2m/k

k=4π^2m/
t^2

When data is inputted, 'k' should equal 141, but when I do it, the number varies and is significantly greater than 141, but starts with those 3 figures. Is it something wrong with the equation or error actually calculating?

My other question is converting s=ut + ½at^2 to y=mx so that I can find out 'a'. I made it so s/t=u+at with s/t equalling 'y', 'a' equalling 'm' and 'x' equalling 't', but the gradient of the graph is about half (not exactly though) what it should be. It should equal 9.81 or whatever gravity's acceleration is, but it equals 4.9532. Have I done the wrong graph then?

 

[neutrino]

For the first, your error must lie in your calculation.

For the second, you can't actually get that equation into the y=mx form, where y is a function of x, because the equation relating s and t is a quadratic, meaning it is an equation of the second degree, and therefore not a straight line.

Other than that, you have missed the 1/2 in the second term, i.e., s/t = u+(a/2t), so that when you eventually get 'a' to one side, your answer of 4.9532 would have been multiplied by 2.

 

[Large dwarf]

For the first, your error must lie in your calculation.

For the second, you can't actually get that equation into the y=mx form, where y is a function of x, because the equation relating s and t is a quadratic, meaning it is an equation of the second degree, and therefore not a straight line.

Other than that, you have missed the 1/2 in the second term, i.e., s/t = u+(a/2t), so that when you eventually get 'a' to one side, your answer of 4.9532 would have been multiplied by 2.

Thanks, I've inputted the data countless times but it continues to equal the wrong number, I might try using Excel instead to calculate.

I know it's not unequivocally a straight line, but the points do form a decent linear line, but you're right, I forgot to divide by two.

Thanks for the help, I may report back here for more help later on, I'm sure you're on the edge of your seat!

 

[Large dwarf]

I'm back already for an open appeal. Using knowledge of 'g' as 9.81 and the spring constant 'k' as 141 (I'll go back to showing these later, can't be arsed to figure the error out yet), I need to find out as much as possible out about bouncing 'bod' (one of those toys which you push down and a few seconds after releasing, they spring into the air). The mass of bouncing 'bod' is 6g, what equations can I use to find out other stuff like what force the spring exerts, how much it compresses or anything like that?

 

[neutrino]

Have you come across Hooke's Law?

 

[jtbell]

When data is inputted, 'k' should equal 141, but when I do it, the number varies and is significantly greater than 141, but starts with those 3 figures.[\quote]

Do you mean you get numbers like 141.2342856, 141.872395, 141.729532? In that case, I would say that the extra digits are almost certainly not significant, given that your measured data is probably good to at most three significant figures in the first place.

Or do you mean you get numbers like 14123.42856, 14187.2395, 14172.9532? In that case, your units are probably inconsistent. Make sure you're not mixing meters and centimeters, or something like that.

 

[Large dwarf]

Have you come across Hooke's Law?

Admittedly no, but a quick look on Wiki told me all I needed to know, cheers again.

I think I've found the strain energy using E=1/2kx^2 now, so that's 2 things done. If I did (2πx)/t would I find the velocity or have I gone down completely the wrong route. I'm not very confident in my ability with equations as you can probably tell.

EDIT: Ignore, I'm using 1/(2π) multiplied by the square root of m/k which I think gives me the frequency.

 

[Large dwarf]

When data is inputted, 'k' should equal 141, but when I do it, the number varies and is significantly greater than 141, but starts with those 3 figures.[\quote]

Do you mean you get numbers like 141.2342856, 141.872395, 141.729532? In that case, I would say that the extra digits are almost certainly not significant, given that your measured data is probably good to at most three significant figures in the first place.

Or do you mean you get numbers like 14123.42856, 14187.2395, 14172.9532? In that case, your units are probably inconsistent. Make sure you're not mixing meters and centimeters, or something like that.

My original figures were:
141711.6689
141763.9242
141802.9631
141132.646
141119.34

but I do believe Excel has solved that small conundrum as I'm now getting figures like the ones you originally suggested, all around the 141 mark, so I am happy.

 

[Large dwarf]

Mass=6g
Spring’s constant is 141 (to 3sf)
‘g’=9.81

Max GPE= mgh
Max GPE= ½kx2

If I need to work out 'x' with the data given, how do I go about it?