[[S.H.M]] Rearranging equations Confusion, Please HELP?

[Jack_Legacy]

[[S.H.M]] Rearranging equations Confusion, Please HELP?

The question that’s got me stuck
Question: A baby of mass = 9kg bounces with a time period of 1.2s in a baby bouncer. What is the spring constant k for the bouncer? Now I know I must rearrange the formula to find k
The formula I/the book used

T = 2π √m ÷ k

I do that and end up with (m × 2π) ÷ T² = k, My book on the other hand rearranges the formula as been (m × 4π²) ÷ T² = k.

Where does the 4π² come from I do not see how 2π changes too 4π², am I missing a rule?
Please help clarify how to get the 4π². I would ask my tutor but he is currently off sick.
My book also does this on the previous question where I am asked to find the value of l in the equation: T = 2π √l ÷ g my book rearranges the equation to (T² × g) ÷ 4π² = k
Again where does the 4π² come from in the original equation.

Thanks you for your help
Jack

 

[dextercioby]

$$T=2\pi\sqrt{\frac{m}{k}}$$

Square this equation.

Daniel.

 

[Jack_Legacy]

maybe a dumb question but, what exactly do you mean? if i square on both sides don't i only cancel the square root and end up with T² on the other side e.g. I'd end up with
T² = 2π (m ÷ k) is this correct

 

[dextercioby]

maybe a dumb question but, what exactly do you mean? if i square on both sides don't i only cancel the square root and end up with T² on the other side e.g. I'd end up with
T² = 2π (m ÷ k) is this correct

Do u agree that $$(ab)^{2}=a^{2}b^{2}$$ ?

If so,apply it...


Daniel.

 

[Jack_Legacy]

still don't quite understand i do agree with that but am quite sure how to apply it, i feel that you won't tell me the exact answer but could you guide me a little closer?

 

[dextercioby]

But of course i won't tell u the answer.The point is to help u find it by yourself.
HINT:
$$(2\pi)^{2} =...??$$,knowing that:
$$(ab)^{2}=a^{2}b^{2}$$

Daniel.

 

[Jack_Legacy]

Okay i think i have it: so if
T = 2π √m ÷ k and we want to find k then:
2π ÷ T = √m ÷ k then we square both sides
(2π ÷ T)² = (√m ÷ k)² which simplified is 4π² ÷ T² = m ÷ k
we then bring over the m and end up with m × 4π² ÷ T² = k
is that correct?

 

[dextercioby]

If it's something like that
$$k=\frac{4\pi^{2}m}{T^{2}}$$

,then it's okay.


Daniel.