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)