A classical mechanics problem by Milun Moghe

In a certain hypothetical space there exists a plane SCOD in which a point source exists at S which radiates light radially only in the given plane. The long line segments extended even after OC and OD have equal masses m=3^0.5 and are hinged about O. OC and OD uniformly distributed masses and are perfect ideal light reflectors. Internal bisector of the two lines is shown by an imaginary dotted line.An arc EGF made of some compressible material and is a perfect absorber of light .

Any light radiation falling on the arc at any angle is absorbed completely. Out of all the light rays emitted from the source of power P=1watt the initial path of two rays are given.

At t=0 the source is switched ON. By some mechanism inside the part EOFG is an energy converter and oscillator which makes the lines oscillate with a very small amplitude with some instantaneous frequency (through an axis perpendicular to the given plane passing through O at time t=0) given by


Here K is constant \[P_{a}=Power(absorbed)\] ,d is the distance of the fixed source from the fixed imaginary axis (internal bisector of the lines of dotted lines)

The lines even though oscillate do not affect the circular shape of the arc only angle is reduced or increased

\[SM=5units\] , \[BO=b=100units\] M is a foot of pipendicular dropped on the axis from the source

\[AO=a=\frac{100}{3^{0.5}}units\] \[EO=GO=FO=50units\] \[tan\theta_{2}=\frac{1}{3^{0.5}}\] \[tan\theta_{1}=3^{0.5}\]

initially \[\alpha=\frac{\pi}{20}\]

Find the instantaneous frequency at t=7 seconds... the value of k=64

Neglect any other radiations and assume reflecting properties of light same as that when reflector is at rest , at all instants of time.


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