| Out of the following functions representing motion of a particle which represents SHM [AIPMT (S) 2011] |
| I. \[y=\sin \omega t-\cos \omega t\] II. \[y={{\sin }^{3}}\omega t\] |
| III. \[y=5\cos \left( \frac{3\pi }{4}-3\,\omega t \right)\] IV. \[y=1+\omega t+{{\omega }^{2}}{{t}^{2}}\] |
A) Only (IV) does not represent SHM
B) (I) and (III)
C) (I) and (II)
D) Only (I)
Correct Answer: C
Solution :
| For a simple harmonic motion |
| \[\frac{{{d}^{2}}y}{d{{t}^{2}}}\propto -y\] |
| Hence, equation \[y=\sin \omega t-\cos \omega t\] and \[y=5\cos \left( \frac{3\pi }{4}-3\omega t \right)\] are satisfying this condition and equation \[y=1+\omega t+{{\omega }^{2}}{{t}^{2}}\] is not periodic and \[y={{\sin }^{3}}\omega t\] is periodic but not SHM. Option is correct. |
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