The angle that the string of a simple pendulum makes with the vertical varies with time according to the equation = 90 [( s ⁻¹) t] . Determine the length of the pendulum, taking g = ^2 m/s ^2 .

Step-by-step solution

The given equation for the angular displacement of the simple pendulum is = 90 ( t) . Comparing this with the standard equation of simple harmonic motion = ₀ ( t) , the angular frequency is = rad/s . The angular frequency of a simple pendulum is given by = g l . Squaring both sides gives ^2 = g l . Rearranging for the length l , we get l = g ^2 . Substituting g = ^2 m/s ^2 and = rad/s into the expression: l = ^2 ^2 = 1 m .