Fig.3. Passive linear elements of translational motion (a) Mass (b) Dash pot (c) Spring. is an element which opposes motion due to friction. If the friction is viscous Dash pot:This 2. friction, the frictional force is proportional to This force is also known as damp ling velocity. force. Thus we can fB = Bv = B (dx/dt) Where B is the damping coefficient. This element is called as dash pot and is symbolically represented as in Fig.(b) 3. Spring:The third element which opposes motion is the spring. The restoring force of a spring is proportional to the displacement. Thus fK = K x Where K is known as the stiffness of the spring or simply spring constant. The symbol used for this element is shown in Fig.(c) (b) Rotational systems:Corresponding to the three basic elements of translation systems, there are three basic elements representing rotational systems. 1. Moment of Inertia:This element opposes the rotational motion due to Moment oflnertia. Theopposing inertia torque is given by, Where and are the angular acceleration, angular velocity and angular displacement a, ω ϴ respectively. J is known as the moment of inertia of the body. 2. Friction:The damping or frictional torque which opposes the rotational motion is given by, Where B is the rotational frictional coefficient. 3. Spring:The restoring torque of a spring is proportional to the angular displacement () and is given by,
Fig.3. Passive linear elements of translational motion (a) Mass (b) Dash pot (c) Spring. 2. Dash pot:This is an element which opposes motion due to friction. If the friction is viscous friction, the frictional force is proportional to velocity. This force is also known as damp ling force. Thus we can fB = Bv = B (dx/dt) Where B is the damping coefficient. This element is called as dash pot and is symbolically represented as in Fig.(b) 3. Spring:The third element which opposes motion is the spring. The restoring force of a spring is proportional to the displacement. Thus fK = K x Where K is known as the stiffness of the spring or simply spring constant. The symbol used for this element is shown in Fig.(c) (b) Rotational systems:Corresponding to the three basic elements of translation systems, there are three basic elements representing rotational systems. 1. Moment of Inertia:This element opposes the rotational motion due to Moment oflnertia. Theopposing inertia torque is given by, Where a, ω and ϴ are the angular acceleration, angular velocity and angular displacement respectively. J is known as the moment of inertia of the body. 2. Friction:The damping or frictional torque which opposes the rotational motion is given by, Where B is the rotational frictional coefficient. 3. Spring:The restoring torque of a spring is proportional to the angular displacement () and is given by,
CS-Lecture-Notes-Units-1-2-3.docx