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b we can make the simple pendulum madel more realistic by adding a damping term to the ordinary differential equation as shown below Lö + yô + g0 = 0 ODE Egn (4) where y is the damping coefficient. Note that when y = 0, we go back to the no damping case. » Write down the auxiliary equation for ODE Egn (4) above and find its roots. ) When considering the case of damping, assume the discriminant of the auxiliary equation is negative. Using the same initial conditions written down in part ai), find a particular solution for the motion of the pendulum in the damping case.

b we can make the simple pendulum madel more realistic by adding a damping term to the ordinary differential equation as shown below Lö + yô + g0 = 0 ODE Egn (4) where y is the damping coefficient. Note that when y = 0, we go back to the no damping case. » Write down the auxiliary equation for ODE Egn (4) above and find its roots. ) When considering the case of damping, assume the discriminant of the auxiliary equation is negative. Using the same initial conditions written down in part ai), find a particular solution for the motion of the pendulum in the damping case.

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Solve b (i, ii) in one hour that i highlighted plz and solve correctly plz and get a thumb up plz
Question 3: Simple Pendulum Figure 3 A simple pendulum consists of a mass m attached to a weightless string of length L (see Figure 3 above). The angle that the pendulum makes with the vertical during its swinging motion is given by 0. a) Using small-angle approximation, the equations of motion of the pendulum can be modelled using 8+20 = 0 ODE Egn (3) where g is the acceleration due to gravity. i) State suitable initial conditions for this model. ii) Using the initial conditions you stated in part a), solve the ordinary differential equation above (ODE Egn (3)] to find a particular solution for the motion. ii) What makes the model above unrealistic? b We can make the simple pendulum model more realistic by adding a damping term to the ordinary differential equation as shown below Lê + yê + g0 = 0 ODE Egn (4) where y is the damping coefficient. Note that wheny = 0, we go back to the no damping case. i) Write down the auxiliary equation for ODE Egn (4) above and find its roots. ii) When considering the case of damping, assume the discriminant of the auxiliary equation is negative. Using the same initial conditions written down in part ai), find a particular solution for the motion of the pendulum in the damping case.
Transcribed Image Text:Question 3: Simple Pendulum Figure 3 A simple pendulum consists of a mass m attached to a weightless string of length L (see Figure 3 above). The angle that the pendulum makes with the vertical during its swinging motion is given by 0. a) Using small-angle approximation, the equations of motion of the pendulum can be modelled using 8+20 = 0 ODE Egn (3) where g is the acceleration due to gravity. i) State suitable initial conditions for this model. ii) Using the initial conditions you stated in part a), solve the ordinary differential equation above (ODE Egn (3)] to find a particular solution for the motion. ii) What makes the model above unrealistic? b We can make the simple pendulum model more realistic by adding a damping term to the ordinary differential equation as shown below Lê + yê + g0 = 0 ODE Egn (4) where y is the damping coefficient. Note that wheny = 0, we go back to the no damping case. i) Write down the auxiliary equation for ODE Egn (4) above and find its roots. ii) When considering the case of damping, assume the discriminant of the auxiliary equation is negative. Using the same initial conditions written down in part ai), find a particular solution for the motion of the pendulum in the damping case.
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