# Tutor profile: Siddharth S.

## Questions

### Subject: MATLAB

Solve the equation $(\dot{x}=xt+t^2+5$) using MATLAB

The solution to the nonlinear ODE can be obtained easily using the MATLAB function ode45. ode45 is a numerical method based on the RK4 method for solving ODEs. ode45 requires a function which estimates and returns the RHS of the governing ODE. This is done using the fuction slope: FUNCTION SLOPE function [F]=slope(t,X) F=X*t+t^2+5; The main program used for specifying the initial condition is given by: MAIN PROGRAM x_in=0; %initial condition delta_t=5; %total time for computation %Solving using ode45 X=ode45(@slope,[0,delta_t],[x_in]);

### Subject: Mechanical Engineering

Why does a cantilever beam with a tip shear load experience nomal stress in the cross sections perpendicular to the axis of the beam?

Consider a beam with a tip shear force in equilibrium. The external forces acting on the beam are: > shear force at the tip > Reaction force at the fixed end The forces are equal in magnitde but opposite in direction. Since the forces are not concurrent, the beam experiences a net bending moment. It is the bending moment and not the shear load that leads to the normal stress developed in the cross sections perpendicular to the axis of the beam.

### Subject: Aerospace Engineering

Explain the importance of the horizontal tail in an aircraft.

During operation, an aircraft mainly experiences four different forces. These forces are: Lift : Aerodynamic force perpendicular to the direction of relative motion Drag: Aerodynamic force parallel to the direction of relative motion Thrust: Force provided by the propulsion system Gravitaional pull of Earth. For a steady flight, the lift force balances the gravitational force while the thrust balances the aerodynamic drag. Since all the forces are balanced by each other, the aircraft does not accelerate. But the forces often lead to some pitching moments about the center of gravity which makes the aircraft unstable. Horizontal tails are components that are used to ensure that the net pitching moment about the center of gravity of the aircraft is zero. They are aerodynamically shaped and hence prduce a lift and drag force when it flows through air. By properly positioning the horizontal tail ( effectively changing the moment arm about cg ), the net pitching moment can be made to be 0, thus providing stability to the aircraft. Also, elevators which are used for maneuvering the aircraft are placed on the horizontal tail.

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