oscillations in mechanical structures and electric circuit

oscillations in mechanical structures and electric circuit can be often
y=exp(-t./j).*sin(w.*t+alpha)
where t is time and w is the oscillation frequency in radians per unit
the oscillations have a period of 2*pi/w , and their amplitudes decay in time
at a rate determined by j , which is called the time constant . the
smaller j is, the faster the oscillations die out .
a- use these facts to develop a criterion for choosing the spacing of the
t values and the upper limit om t to obtain an accurate plot of y(t)
(hint consider two cases 4*j>pi/w and 4*j<2*pi/w )

b- apply your criterion, and plot y for j = 10 w= pi alpha = 2

c- apply your criterion , and plot y for j= 0.1 w=pi alpha= 2