The Caught Pendulum. Suppose the massless rod in the discussion length of the nonlinear

Chapter 3, Problem 17

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The Caught Pendulum. Suppose the massless rod in the discussion length of the nonlinear pendulum is acwally a string of l. A mass mis attached to the end of the string and the pendulum. is released from rest at a small displacement angle 60 > 0. When the pendulum. reaches the equilibrium position OP in Figure 3.11.3 the string bits a nail and gets caught at this point U4 above the mass. The mass oscillates from this new pivot point as shown in FIGURE 3.11.7. (a) Consttuctand solve a linear initial-value problem 1hat gives the displacement angle, denote it lli(t), for 0 t < T, where Trepresents the time when the string first hits the naiL (b) Find the time T in part (a). (c) Construct and solve a linear initial-value problem that where gives the displacement angle, denote it 62(t), for t ;::::: T, Tis the time in part (a). Compare the amplitude and period of oscillations in this case with that predicted by the initial-value problem in part (a). FIGURU.11.7 Peodulumin 17