Login/Sign Up
Home » The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt
The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt
CBSE | Class 11 | NCERT Exemplar | Oscillations | Physics
The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt

a) the motion is oscillatory but not SHM

b) the motion is SHM with amplitude a + b

c) the motion is SHM with amplitude a2 + b2

d) the motion is SHM with amplitude √a2 + b2

Answer:

The correct option is d) the motion is SHM with amplitude √a2 + b2

Explanation:

       …….(i)
Let             ……..(ii)
and             ……….(iii)
Now, squaring and adding (ii)  and (iii), we get the following expression

  {{a}^{2}}+{{b}^{2}}={{A}^{2}}{{\cos }^{2}}\phi +{{A}^{2}}{{\sin }^{2}}\phi

{{a}^{2}}+{{b}^{2}}={{A}^{2}}

x=A\cos \phi \sin \omega t+A\sin \phi \cos \omega t

x=A\sin (\omega t+\phi )

This represents the equation of SHM with amplitude A=\sqrt{{{a}^{2}}+{{b}^{2}}}

 

​

i

More Material