Consider the integro differential equation below, dv_out(t)/dt +20 integral^t_0^- v_out(q)dq=10v_in(q)dq Convert the equation to a purely differential equation. Determine the relationship between V_out(s) and V_in (s), v_in (0^-), and dv_out/dt (0^-_. When the initial conditions are all zero and v_in(0^-) = 0, one can define the relationship H(s) = V_out(s)/V_in(s) associated with the intergo-differential equation. Later we will call H(s) the so-called transfer function meaning that V_out(s) = H(s)V_in(s) when all IC’s are zero. Compute H(s). Given your answers to (a) and (b), show that in the s-world: V_out(s) = H(s)V_in(s) + (Something)v_out(0^-) + (Something – else) dv_out(0^-)/dt

94 1 - Consider the integro differential equation below, dv_out(t)/dt +20 integral^t_0^- v_out(q)dq=10v_in(q)dq Convert the equation to a purely differential equation. Determine the relationship between V_out(s) and V_in (s), v_in (0^-), and dv_out/dt (0^-_. When the initial conditions are all zero and v_in(0^-) = 0, one can define the relationship H(s) = V_out(s)/V_in(s) associated with the intergo-differential equation. Later we will call H(s) the so-called transfer function meaning that V_out(s) = H(s)V_in(s) when all IC's are zero. Compute H(s). Given your answers to (a) and (b), show that in the s-world: V_out(s) = H(s)V_in(s) + (Something)v_out(0^-) + (Something - else) dv_out(0^-)/dt

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images - Consider the integro differential equation below, dv_out(t)/dt +20 integral^t_0^- v_out(q)dq=10v_in(q)dq Convert the equation to a purely differential equation. Determine the relationship between V_out(s) and V_in (s), v_in (0^-), and dv_out/dt (0^-_. When the initial conditions are all zero and v_in(0^-) = 0, one can define the relationship H(s) = V_out(s)/V_in(s) associated with the intergo-differential equation. Later we will call H(s) the so-called transfer function meaning that V_out(s) = H(s)V_in(s) when all IC's are zero. Compute H(s). Given your answers to (a) and (b), show that in the s-world: V_out(s) = H(s)V_in(s) + (Something)v_out(0^-) + (Something - else) dv_out(0^-)/dt

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