Show that v=r`omega`.

Show that a=r omega^(2) .

If |z| <= 1 and |omega| <= 1, show that |z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2

A thin circular loop of radius R rotates about its vertical diameter with an angular frequency omega . Show that a small bead on the wire loop rem ains at its lowermost point for omega oversetlarrsqrt(g/R) What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for omega = sqrt (2g/R) ? neglect friction.

Show that the average power transferred to an a.c. circuit is in general given by P= V_(r.m.s) I _(r.m.s) R//Z . Where R is the resistance in the circuit.

Show that the straight lines whose direction cosines are given by the equations a l+b m+c n=0 and u l^2+z m^2=v n^2+w n^2=0 are parallel or perpendicular as (a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.

Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 muF , R= 40 Omega . Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency. :

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot

The displacemnt of a particle inS.H.M. may be given by y = r sin (omegat + phi_0) . Show that if the time t is increased by (2pi)/omega the value of y remains unchanged.

Let omega be a complex cube root of unity with omega ne 1 . A fair die is thrown three times. If r_(1), r_(2) and r_(3) are the numbers obtained on the die, then the probability that omega^(r_(1)) + omega^(r_(2)) + omega^(r_(3)) = 0 is