(Solved):   QUESTION 1 A foot pedal mechanism for a machine is crudely modelled as a pendulum connecte ...

 

QUESTION 1 A foot pedal mechanism for a machine is crudely modelled as a pendulum connected to a spring. It will be subjected to wind loads producing an applied force of F(t)=F, cos wt, where the largest value of Fo is measured to be 15 N. This is illustrated on the right side of Figure Q1. The purpose of the spring is to provide a return force for the pedal action. Assume that the angular deflections are small, such that the arc length can approximate the spring deflection, that the pedal may be treated as a point mass, and that the pendulum rod has negligible mass. The pedal is horizontal when the spring is at its free length. The values in the figure are m = 2.5 kg, w = 14.4 rad/s, k= 2500 N/m. 1? = 0.2m and 1? = 0.8m. 1.4 Write down the differential equation of motion of the system in terms of 0. 1.5 Determine the natural frequency of the system for small oscillations. 1.6 Determine the maximum amplitude of vibration at A due to the varying load. (10) (2) (3) 1? F(t) 1? g 0000 0 Figure Q1 m [15 marks]