Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear
Question:
Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear pendulum (see description in Prob. 23.10). Compute the period for the following initial conditions:
(a) θ = π / 8,
(b) θ = π / 4, and
(c) θ = π / 2.
For all three cases, set the initial angular velocity at zero.
Data from in problem 23.10
Transcribed Image Text:
23.10 The oscillations of a swinging pendulum can be sim- ulated with the following nonlinear model: d²0 d1² + sin 0 = 0 0 where = the angle of displacement, g = the gravitational constant, and I = the pendulum length. For small angular displacements, the sin is approximately equal to and the model can be linearized as d²0 dt² +0=0 Use ode45 to solve for as a function of time for both the linear and nonlinear models where 1 = 0.6 m and g = 9.81 m/s². First, solve for the case where the initial condition is for a small displacement (0 = 7/8 and de/dt = 0). Then repeat the calculation for a large displace- ment (0 = 7/2). For each case, plot the linear and nonlinear simulations on the same plot.
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Related Book For
Applied Numerical Methods With MATLAB For Engineers And Scientists
ISBN: 9781259027437
3rd Edition
Authors: Steven C. Chapra
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