ClearAll["global`*"];
m = 1.0 ; g = 9.8 ; r = 1.0 ; 
u[theta_, b_] := m g ((r + b) Cos[theta] + r theta Sin[theta]);

Plot[u[theta, 0.9], {theta, -Pi/2, Pi/2}]

Manipulate[
Plot[u[theta, b], {theta, -Pi/2, Pi/2}],
{b, 0.1, 1.5, Appearance -> "Labeled", LabelStyle->Large}]