Question

In the system shown, a long uniform rod is attached at one end of a spring constant k and the other end is hinged. It is displaced slightly and allowed to oscillate. The time period of oscillation is

• A. $2 \pi \sqrt { \frac { M } { k } }$
• B. $2 \pi \sqrt { \frac { M } { 2 k } }$
• C. $2 \pi \sqrt { \frac { M } { 3 k } }$
• D. None of these

Answer 1

Answer: (C)

$2 \pi \sqrt { \frac { M } { 3 k } }$

Answer 2

τ = kyl = kl²θ

therefore,

$\frac { M l ^ { 2 } } { 3 } \alpha = - k l ^ { 2 } \theta$

or

T=$2 \pi \sqrt { \frac { M } { 3 k } }$