1. The problem statement, all variables and given/known data 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/ [Broken] Remaining part of the question should be on second page of my homework. 2. Relevant equations v^2=2*G*L*cos(theta) 3. 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.