Question

A very light rigid rod with a length of 0.411 m extends straight out from one end of a meter stick. The combination is suspended from a pivot at the upper end of the rod as shown in the following figure. The combination is then pulled out by a small angle and released (a) Determine the period of oscillation of the system. 2.09 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.s b) By what percentage does the period differ from the period of a simple pendulum 0.911 m longi? 8.61 Your response differs from the correct answer by more than 10%. Double check your calculations.%

Answer 1

(A) Icm = m L^2 / 12

I = Icm + m (L/2 + l)^2 = m L^2 / 12 + m (L/2 + 1)^2

I = m (1^2 /12 + (0.5 + 0.411)^2)

I = 0.91325 m

d_cm = d = 0.411 + 0.50 = 0.911 m

T = 2 pi sqrt[ I / m g d ] = 2 pi sqrt[ 0.9135 / (9.8 x 0.911)]

T = 2 sec ....Ans

(B) T' = 2 pi sqrt[ L / g] = 1.916 sec  

% = (T - T')/T x 100

= 4.2 %