Given the system with an impulse response function

ℎ[w] = 3e^−20t use the convolution integral to calculate the response to the input x[t] = 10cos(10t) for t>0. Also, calculate the steady state response using phasor analysis, given that the frequency response

function of the system ℎ[w] = 3/(20+jw)

Hint

Using the convolution integral:

y[t] = ∫(from 0 to t) ℎ[ t - tau ]x[tau}d(tau)= (requires a recursion formula,and has steady state and transient parts)

Using Phasor analysis:

y[w] = ℎ[ w= 10]x[w = 10] =? (yields steady state solution)