Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
The differential equation of motion for a single degree of freedom mass-spring damped system is 8(d²x/dt²) + 5(dx/dt) + 12x = 0. If the units of mass, length and time are kg, m, and s respectively, the natural frequency of vibration is
Options:
(A) 0.42 rad s⁻¹
(B) 0.52 rad s⁻¹
(C) 1.22 rad s⁻¹
(D) 1.83 rad s⁻¹
Official Answer Key:
C
Step-by-Step Solution & Explanation
For m·ẍ+c·ẋ+k·x=0, the undamped natural frequency ωn = √(k/m) = √(12/8) = √1.5 = 1.2247 rad/s.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.