Question

7.6: Impulses/delta functions 20. Explain what is a delta function and why do we care about it? A box with mass 1 and spring constant 4 is hit by an instantaneous force imparting 2 units of momentum at time . Suppose that (0) = 0 and x'(0) = 1. Find a(t).

Answer 1

for any xlo)=0 Drac Delta Function :-) Slt) is define by tto (۱) s(t)= ? infinite t=0 and tamation (2) $(+) 5(+) dt = f (0) ft) antinious and containo Solm x' +48=2.8(+-*) xlo=1 Let {(*) 5= x(s) (2) ² x(s)-solo) – x(0) ES? x (s)-5.0-1. take Laplace trasteron $? x (s)-1 +4 x(s) £286+-1) x(s) (5²+4) а е 2 --- = = - TIS = +1. - TIS x(s)=2 2 + 2 544 st4 take inverse 2e-T15 +2 2 st2² Š (x(s)) = 5²72² a(t) sn/2(t-1)) u (4-71) + x(+) = sin(at-2T) + 1/ sinat sinat tot =) t<T. sinat et 3 sin(at) to t 2 - a (+) = ) et elu sinat t<T २

!! PLEASE VOTE THUMBS UP !!