Ques. 1AIPMT 2011 (Prelims)
Out of the following functions representing motion of a particle which represents SHM (1) y = sin t - cos t (2) y = sin3 t (3) y = 5 cos ( 3 4 - 3 t ) (4) y = 1 + t + 2 t2
- Only (1)
- Only (4) does not represent SHM
- Only (1) and (3)
- Only (1) and (2)
Answer
(3) Only (1) and (3)
Solution
A motion is SHM only if it can be written as a single sine or cosine function of time, i.e. a = - 2 y.
(1) y = sin t - cos t
y = 2 sin ( t - 4 ), so it is SHM.
(2) y = sin3 t = 3 sin t - sin 3 t4, which is the sum of two SHMs of different frequencies, so it is periodic but not SHM.
(3) y = 5 cos ( 3 4 - 3 t ) is a single cosine function of angular frequency 3 , so it is SHM.
(4) y = 1 + t + 2 t2 grows without limit, so it is not even periodic and hence not SHM.
Only (1) and (3) represent SHM.
Answer: (3)