## Problem 2.4 Loci of Points – A pendulum OC is pivoted at O is 120 mm long. It swings 30^{0} to the right of vertical and also 30^{0} to the left of vertical. An insect initially at O reaches to the point C, when the pendulum completes two oscillations. Draw the path of the insect, assuming motion of the insect and pendulum as uniform.

*Procedure:*

* Step-1* First mark a point O and draw a vertical line from it of the length 120 mm, which is equal to the length of the pendulum. And at the end of the line mark a point C

_{0}.

* Step-2* Draw three vertical lines on the left and right sides from O of the length equal to OC

_{0}, at an angle 10°from each other as shown into the figure.

* Step-3* Now the total degree (°) covered by the pendulum in completing the two oscillations is 240°. So, the total degree covered by the pendulum and the length of the pendulum should be divided into the same number of divisions. That’s why the total degree covered by the pendulum and the length of the pendulum have been divided into 24 equal divisions.

Note: It can be divided in any convenient number of divisions but it should be rounded number

* Step-4* Now divide the length of the pendulum into 24 equal divisions and give the notations 1,2,3, etc. as shown into the figure. And give the notations at the end of the lines as C

_{1}, C

_{2}, C

_{3}etc. in any direction but they must be in sequence.

* Step-5* With O as center and radii equal to O1, O2, O3 etc. draw arcs between the respective lines, like OC

_{1}, OC

_{2}, OC

_{3}etc. as given into the figure.

* Step-6* Now connects the end points of the arcs drawn into sequence by a smooth medium dark free hand curve to get the locus of the path of the insect.

* Step-7* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.