The displacement of a moving particle at any time t is given by y = a cost+b sint. Show that the motion is simple harmonic.
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Answer:
Given,
y=A
0
+Asinωt+Bsinωt
Equation of SHM
$$y' = y - A_0 = A sin \omega t + B cos \omega t$$
Resultant amplitude,
R=
A
2
+B
2
+2ABcos90
∘
=
A
2
+B
2
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