[Solved] Let f satisfy f(t+T)=f(t) for all t>0 and for some fixed positive number T; f is said to be periodic with period T on 0≤t<∞

Let f satisfy f(t+T)=f(t) for all t>0 and for some fixed positive number T; f is said to be periodic with period T on 0≤t<∞. Then, the Laplace transform of f(t) is given by L{f(t)}=11−e−sT∫0Te−stf(t)dt.

Use this fact to find the Laplace transform of the given function.

f(t)={ 1, 0≤t<4

{ -1, 4≤t<8

f(t+8)=f(t)

Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

Use an asterisk, *, to indicate multiplication. For example, 2*f(x), a*x*(x+b)*(c*x+d), b*tan(a*θ) or e(a*x)*b.

Expert Answer

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Answer to Let f satisfy f(t+T)=f(t) for all t>0 and for some fixed positive number T; f is said to be periodic with period T on 0≤t<∞…..