Question
If displacement of a particle at any instant is represented by y = A cos ωt + B sin ωt, where A and B are constants, prove that the motion of particle is simple harmonic motion. What is the amplitude and epoch of the motion?
Solution
Position of particle is given by,
y = A = cos
+ B sin
...(1)
The velocity of particle is given by,
Acceleration of particle is given by,
Since the acceleration of particle is directly proportional to displacement and directed towards mean position, therefore the motion is simple harmonic motion.
Now, 
Squaring (2) and (3) and adding, we have
Dividing (2) (3), we have
Epoch = 
