Question

For a simple harmonic motion with given angular frequency `omega`, two arbitrary initial conditions are necessary and sufficient to determine the motion completely. These initial conditions may be
A. initial position and initial velocity
B. amplitude and initial phase
C. total energy of oscillation and amplitude
D. total energy of oscillation and initial phase.

Answer 1

Correct Answer - A::B::D
Description of motion is completely specified if we know the variation of x as a function of time. For simple harmonic motion, the general equation of motion is `x=A(omegat+delta)`. As `omega` is given to describe the motion completely, we need the values of A and `delta`. From options (b) and (d) we can have the value of A and `delta` derectly. For option (a) we can find A and `delta` if we know initial velocity and initial position. Option (c ) cannot give the value of A and `delta` so it is not the correct condition.