- A Vibrating System Is Modelled By A 1 5m Long Rigid Bar Of Mass 0 75kg Supported On A Pivot Bearing As Shown In Figure Q 1 (73.39 KiB) Viewed 32 times
A vibrating system is modelled by a 1.5m long rigid bar of mass 0.75kg supported on a pivot bearing as shown in Figure Q1. The bar has 2 masses, mi and m2, (1kg and 2kg) attached and springs of stiffness k and k2 (500N/m and 750N/m) connect the masses to the supports. The masses are set on frictionless rollers. (a) In terms of the parameters k, m, L and write down expressions for i. The Kinetic Energy of the system ii. The Potential Energy of the system (6) (b) Derive the equation of motion of the system. (6) (c) Determine the values for the inertia and stiffness of the system. (2) (d) Give the expression for and determine the natural frequency of the system in Hertz. (3) (e) A torsion damper is to be fitted to help control vibrations. Determine the value of the damping coefficient required if the system when given an initial displacement returns to its equilibrium position in the shortest time without overshooting. (3) (1) Determine the amplitude of the vibrations in degrees when a sinusoidal torque of 400NM is applied at the pivot at a frequency of 5Hz. (5) find mi pivot 243 rüt m2 Figure Q1 A detailed view of the vibrating system