A measurement device is constructed from two (identical) uniform bars, welded together at right angles and pivoted about a horizontal axis through point O as illustrated in Figure Q3. Each of the bars has mass m, and each end of the horizontal bar is supported by identical springs, each of stiffness k, and both of which are connected to a solid surface. A torsional damper with damping coefficient, ce, is applied at the pivot at O. A horizontal force of magnitude F (t) = 4.59e¬t, (where t is the time in seconds), is now applied to the end of the vertical bar as illustrated, causing the system to rotate. Q3 (a) Show that the moment of inertia of the welded bars about the pivot O is given by ml?. 12 (b) Assuming that neither spring is extended when the system is stationary, find the equation of motion of the system. (c) The system has the following properties: k = 81.5 N/m; L=56 cm; Ce = 0.79 Nms/rad ; т — 780 grammes With the force, F(t), as given above, determine if the system is sub-critically damped or overdamped, and determine the natural frequency of oscillation, Wn. (d) Using a Laplace Transform approach, determine the response of the system, e(t), to the applied force, F(t). You may assume that gravitational acceleration, g = 9.81 m/s², and that the small angle approximation may be used throughout. L/2 L/2 0 +ve

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Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.