Question

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

(a) x = Acosωt + B sinωt

(b) x = (A+B)cosωt

(c) x = (A+B)sinωt

(d) x = Atanωt + B sinωt

I got this question by my college professor while I was bunking the class.

Origin of the question is Differential Equation of Simple Harmonic Motion topic in chapter Simple Harmonic Motion of Machine Kinematics

Answer 1

The correct answer is (a) x = Acosωt + B sinωt

The best explanation: We know that dx/dt = -Aωsinωt

d^2x/dt^2 = -aω^2cosωt

therefore

d^2x/dt^2 + ω^2x = 0

is the standard differential equation of Simple Harmonic Motion

It’s solution is/are:

x = Acosωt + B sinω