Solution Found!
e 4.18 is released from rest at the angle ,0 < < , then
Chapter 4, Problem 10E(choose chapter or problem)
PROBLEM 10EUse the result of to prove that if the pendulum in Figure 4.18 is released from rest at the angle ?,0 < ? < ?, then |?(t)| ? for all t. [Hint: The initial conditions are ?(0)=?,?’(0)=0; argue that the constant in equals –(g/l) cos ?.]
Questions & Answers
QUESTION:
PROBLEM 10EUse the result of to prove that if the pendulum in Figure 4.18 is released from rest at the angle ?,0 < ? < ?, then |?(t)| ? for all t. [Hint: The initial conditions are ?(0)=?,?’(0)=0; argue that the constant in equals –(g/l) cos ?.]
ANSWER:SolutionStep 1In this problem we have to prove that ,when then | for every t. Where t = time = initial position of the pendulum i.e. angle made by the pendulum with the vertical axis at time t =0 = angle made by the pendulum at time t with the vertical axis of the pendulum at time t. l = length of the pendulum m = mass of the bob