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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 1/4 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 that gives the displacement angle, denote it 01(t), for 0≤t< T, where T represents the time when the string first hits the nail. (b) Find the time Tin 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 nail U4

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 1/4 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 that gives the displacement angle, denote it 01(t), for 0≤t< T, where T represents the time when the string first hits the nail. (b) Find the time Tin 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 nail U4

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Q#2 Please solve correctly, NOT using Laplace method
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 1/4 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 that gives the displacement angle, denote it 01(t), for 0 <t< T, where T 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 t2T, 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 nail 14
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 1/4 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 that gives the displacement angle, denote it 01(t), for 0 <t< T, where T 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 t2T, 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 nail 14
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