Question 2 A student, thoroughly bored by the lecture on applications of log decrement, clamps one end of his ruler to t

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Question 2 A Student Thoroughly Bored By The Lecture On Applications Of Log Decrement Clamps One End Of His Ruler To T 1 (75.64 KiB) Viewed 47 times

Question 2 A student, thoroughly bored by the lecture on applications of log decrement, clamps one end of his ruler to the desk using his left hand. He applies a static force to the other end of the cantilevered ruler with his index finger of his right hand. He notes with considerable interest that a force of 3.5 N results in a deflection of 36 mm at the end of the ruler under his finger. He allows his finger to slip from the end of ruler resulting in a loud 'twanging' noise. The lecturer stares at him momentarily and then ignores him. The student reflects upon the fact that five oscillations of the end of the ruler take exactly 0.75 seconds i.e.750 milliseconds. Also, after the five oscillations, the amplitude of the oscillations of the ruler tip has reduced from 36 mm to 6 mm. (He has very good eyesight.) He now applies a steady sinusoidal force with amplitude 3.5 N to the end of the ruler at a frequency of 10 Hz. (He suffers from a nervous ailment.) Assume that the cantilevered ruler can be treated as a single degree of freedom mass-spring-damper system. (a) What is the non-dimensional damping factor for the system? (b) What is the undamped natural frequency? (6 marks) (It is not necessary to check your calculations through experiment.) (4 marks) (c) What is the amplitude of the forced vibration when it is excited at 10 Hz? (10 marks) L