Simplify this expression for the period

[crememars]

Homework Statement

A bob of mass m is suspended from a fixed point with a massless string of length L. You are to investigate the motion in which the string moves in a cone with half-angle, 𝜃. Express your answers in terms of some or all of the variables m, L, and 𝜃, and g.

v = √Lgsin𝜃tan𝜃

How long does it take the bob to make one full revolution (one complete trip around the circle)?

Relevant Equations

T = 2πr / v
r = Lsin𝜃

hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my math notes too.

my expression for T is:

T = 2πLsinθ / √(Lgsinθtanθ)
T = 2πLsinθ * √(Lgsinθtanθ) / Lgsinθtanθ
T = 2π * √(Lgsinθtanθ) / gtanθ

final answer

[ 2π * √(Lgsinθtanθ) ] / gtanθ

the correct answer should be:

2π * √( Lcosθ / g )thank you in advance

 

[BvU]

Hi,

How about the forces that act on the bob ? Can you draw a diagram ?

$\$

 

[kuruman]

If you square the denominator, you can put it inside the radical. What do you get?

 

[crememars]

If you square the denominator, you can put it inside the radical. What do you get?

tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it

 

[kuruman]

tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it

It's called "taking the square root" or "squaring". You can go back and forth in what is shown below.
$$\sqrt{\frac{A}{B^2}}=\frac{\sqrt{A}}{\sqrt{B^2}}=\frac{\sqrt{A}}{B}$$