Question

Which of the following is the correct differential equation of the SIMPLE HARMONIC MOTION?

(a) d^2x/dt^2 + ω^2x = 0

(b) d^2x/dt^2 – ω^2x = 0

(c) d^2x/dt + ω^2x = 0

(d) d^2x/dt – ω^2x = 0

This question was posed to me during a job interview.

This intriguing question originated from Differential Equation of Simple Harmonic Motion in portion Simple Harmonic Motion of Machine Kinematics

Answer 1

Right choice is (a) d^2x/dt^2 + ω^2x = 0

The explanation: For body undergoing Simple Harmonic Motion, it’s motion can be represented as projected uniform circular motion with radius equal to the amplitude of motion.

Therefore x =Acosωt

dx/dt = -Aωsinωt

d^2x/dt^2 = -aω^2cosωt

therefore

d^2x/dt^2 + ω^2x = 0