GATE 2017 ME (ME2) – Question 41
A compound pendulum has radius of gyration 100 mm about its suspension point. The suspension-to-centre-of-mass distance is 250 mm. With g = 9.81 m/s², its natural frequency is ______ rad/s.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 15 to 16
Explanation
Small-angle equation is I(O)θ-double-dot+mglθ=0. With I(O)=mk(O)², angular frequency is√(gl/k(O)²)=√(9.81·0.25/0.1²)=**15.66rad/s**, consistent with the official15–16 range. However, the stated radius about the suspension is smaller than the centre-of-mass distance; those dimensions cannot describe a physical rigid pendulum.