Pendulum problem concerning the spring constant

[Benzoate]

Homework Statement

The velocity of the mass at the end of the arm is v^2=2*g*cos(theta) , where theta is the angle the arm makes with the vertical, and we assumed that the arm is rigid and massless. ... I will post the link that has the remaining part of my question since its difficult for me to right "r hat" and "theta hat" Just using character symbols.

http://courses.ncsu.edu/py411/lec/001/

Remaining part of the question should be on second page of my homework.

Homework Equations

v^2=2*G*L*cos(theta)

The Attempt at a Solution

differentiating v^2 , I get v=-g*sin(theta)

a=(2g *cos(theta))"r-hat" - (g sin(theta))"theta hat", a being the acceleration. My acceleration will be in the "r-hat" and "theta hat" polar coordinates rather than cartesian coordinates. since theta is soooooooo small, cos(theta) approximates to 1 and sin(theta) approximates to 0. Therefore , a = 2g"r hat" +0"theta hat"=> a=2g"rhat". I don't understand why the problem just say that a= K*x rather than defined K*x to be the second derivative of the position vector, since I do not need to derived the position vector twice to get the acceleration vector. Mot sure what K real symbolizes is this problem. In this problem, they want me to show the equation of motion in the form of a spring , so I guess then k=sqrt(g/L), but would I need to write out K explicitly? In addition, the Forces of the pendulum would be in the theta hat and r hat direction .

r hat: T-mg cos(theta)=m*a

theta hat:=-mg*sin(theta)=m*a

So I should be able to find my Tension now right? I'm not even sure if the Forces of the pendulum are relevant to this problem.

 

[Benzoate]

Homework Statement

The velocity of the mass at the end of the arm is v^2=2*g*cos(theta) , where theta is the angle the arm makes with the vertical, and we assumed that the arm is rigid and massless. ... I will post the link that has the remaining part of my question since its difficult for me to right "r hat" and "theta hat" Just using character symbols.

http://courses.ncsu.edu/py411/lec/001/

Remaining part of the question should be on second page of my homework.

Homework Equations

v^2=2*G*L*cos(theta)

The Attempt at a Solution

differentiating v^2 , I get v=-g*sin(theta)

a=(2g *cos(theta))"r-hat" - (g sin(theta))"theta hat", a being the acceleration. My acceleration will be in the "r-hat" and "theta hat" polar coordinates rather than cartesian coordinates. since theta is soooooooo small, cos(theta) approximates to 1 and sin(theta) approximates to 0. Therefore , a = 2g"r hat" +0"theta hat"=> a=2g"rhat". I don't understand why the problem just say that a= K*x rather than defined K*x to be the second derivative of the position vector, since I do not need to derived the position vector twice to get the acceleration vector. Mot sure what K real symbolizes is this problem. In this problem, they want me to show the equation of motion in the form of a spring , so I guess then k=sqrt(g/L), but would I need to write out K explicitly? In addition, the Forces of the pendulum would be in the theta hat and r hat direction .

r hat: T-mg cos(theta)=m*a

theta hat:=-mg*sin(theta)=m*a

So I should be able to find my Tension now right? I'm not even sure if the Forces of the pendulum are relevant to this problem.

How come no one has answered my question yet? Is it too long? Is there something wrong with my wording?

 

[Kurdt]

How come no one has answered my question yet? Is it too long? Is there something wrong with my wording?

Well first its only been 13 hours since you posted and secondly, you never linked directly to your homework questions so people are going to be confused when they don't find it. I'll link to it here: http://courses.ncsu.edu/py411/lec/001/PY411-HW2-08.pdf

The pendulum is subject to an acceleration and its position is given in terms of theta by $L \theta$. The acceleration of the bob along that path must be equal to the acceleration you derived previously (in your notes). Note that you can ignore the r components.