1. Derive the equations of motion of a triple pendulum as shown below using Lagrange's equations....

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1. Derive the equations of motion of a triple pendulum as shown below using Lagrange's equations. l m m . m 2. A spring-mass-damper system is shown below. The system has a single mass and spring with spring constant k and a damper with damping constant c. k www x(t) C m (a) Solve for the equations of motion for the system (b) Write a matlab code to plot the phase space of the system for three cases below over a time t = 0 to 30 seconds with a time step of 0.1. Use ODE45 function in MATLAB (i) c = 0 (no damping) (ii) c = 0.1 (iv) c = 1 Ns/m Note: Use k=1 N/m,m=1 kg and initial conditions of displacement = 0 and velocity = 1 m/s for all three conditions. 1. Derive the equations of motion of a triple pendulum as shown below using Lagrange's equations. l m m . m 2. A spring-mass-damper system is shown below. The system has a single mass and spring with spring constant k and a damper with damping constant c. k www x(t) C m (a) Solve for the equations of motion for the system (b) Write a matlab code to plot the phase space of the system for three cases below over a time t = 0 to 30 seconds with a time step of 0.1. Use ODE45 function in MATLAB (i) c = 0 (no damping) (ii) c = 0.1 (iv) c = 1 Ns/m Note: Use k=1 N/m,m=1 kg and initial conditions of displacement = 0 and velocity = 1 m/s for all three conditions.