Q1 A pendulum is modelled by a mass that is attached to a weightless rigid rod. According to Newton's second law, as the pendulum swings back and forth, the sum of the forces that are acting on the mass equals the mass times acceleration. The equilibrium equation in the tangential direction as: EF, =-CL-mg sine = mLd d²e di² Where angle of the pendulum (with respect to the vertical axis, as shown in the figure) c=0.16(N-s)/m is the damping coefficient, m=0.5kg is the mass, L-1.2m is the length, and g-9.81m/s² is the acceleration due to gravity. The pendulum is initially displaced such that 0=90°, and then at t=0 it released from rest, d = 0 (zero initial velocity). Determine the angle de dt of the pendulum at 0.1 second using Runge-Kutta 2nd Order Method (Heun's method ) and step size (h=0.02). y 11-0 L ។ K²₂² = f(tish, j²h;2;²²) 0
Q1 A pendulum is modelled by a mass that is attached to a weightless rigid rod. According to Newton's second law, as the pendulum swings back and forth, the sum of the forces that are acting on the mass equals the mass times acceleration. The equilibrium equation in the tangential direction as: EF, =-CL-mg sine = mLd d²e di² Where angle of the pendulum (with respect to the vertical axis, as shown in the figure) c=0.16(N-s)/m is the damping coefficient, m=0.5kg is the mass, L-1.2m is the length, and g-9.81m/s² is the acceleration due to gravity. The pendulum is initially displaced such that 0=90°, and then at t=0 it released from rest, d = 0 (zero initial velocity). Determine the angle de dt of the pendulum at 0.1 second using Runge-Kutta 2nd Order Method (Heun's method ) and step size (h=0.02). y 11-0 L ។ K²₂² = f(tish, j²h;2;²²) 0
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Q1
A pendulum is modelled by a mass that is attached to a weightless rigid rod. According to
Newton's second law, as the pendulum swings back and forth, the sum of the forces that are
acting on the mass equals the mass times acceleration. The equilibrium equation in the
tangential direction as:
EF, -CL
do
dt
-mg sin0 = mL
Ld²o
di²
Where angle of the pendulum (with respect to the vertical axis, as shown in the figure)
c=0.16(N-s)/m is the damping coefficient, m=0.5kg is the mass, L-1.2m is the length, and
g-9.81m/s² is the acceleration due to gravity. The pendulum is initially displaced such that
0-90°, and then at t=0 it released from rest, = 0 (zero initial velocity). Determine the angle
of the pendulum at 0.1 second using Runge-Kutta 2nd Order Method (Heun's method ) and
step size (h=0.02).
de
dt
1-1-0
D
0
។
K²₂² = f(tish, Off²h, 2; thks")
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