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Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of length I. A mass m is attached to the end of the string and the pendulum. is released from rest at a small displacement angle 00> 0. When the pendulum. reaches the equilibrium position, the string hits a nail and gets caught at this point U4 above the mass. The mass oscillates from this new pivot point as shown in the figure. (a) Construct and solve a linear initial-value problem 1hat gives the displacement angle, denote it 01(t), for 0 ≤1

Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of length I. A mass m is attached to the end of the string and the pendulum. is released from rest at a small displacement angle 00> 0. When the pendulum. reaches the equilibrium position, the string hits a nail and gets caught at this point U4 above the mass. The mass oscillates from this new pivot point as shown in the figure. (a) Construct and solve a linear initial-value problem 1hat gives the displacement angle, denote it 01(t), for 0 ≤1

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Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of length 1. A mass m is attached to the end of the string and the pendulum. is released from rest at a small displacement angle 00 > 0. When the pendulum. reaches the equilibrium position, the string hits a nail and gets caught at this point U4 above the mass. The mass oscillates from this new pivot point as shown in the figure. (a) Construct and solve a linear initial-value problem 1hat gives the displacement angle, denote it 01(t), for 0 ≤t< T, where represents 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 gives the displacement angle, denote it 02(t), for t≥T, where T is 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). 00 V4 nail
Transcribed Image Text:Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of length 1. A mass m is attached to the end of the string and the pendulum. is released from rest at a small displacement angle 00 > 0. When the pendulum. reaches the equilibrium position, the string hits a nail and gets caught at this point U4 above the mass. The mass oscillates from this new pivot point as shown in the figure. (a) Construct and solve a linear initial-value problem 1hat gives the displacement angle, denote it 01(t), for 0 ≤t< T, where represents 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 gives the displacement angle, denote it 02(t), for t≥T, where T is 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). 00 V4 nail
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