NEET-XII-Physics
12: Simple Harmonic Motion
- #7The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is
(a) not simple harmonic
(b) simple harmonic with amplitude A + B
(c) simple harmonic with amplitude (A + B)/2
(d) simple harmonic with amplitude
A2+B2.digAnsr: dAns : (d) simple harmonic with amplitude A sin ωt + B cos ωt ...(1)
`` \,\mathrm{\,Acceleration\,},``
`` a=\frac{{d}^{2}x}{d{\,\mathrm{\,t\,}}^{2}}=\frac{{d}^{2}}{d{\,\mathrm{\,t\,}}^{2}}(A\,\mathrm{\,sin\,}\omega t+B\,\mathrm{\,cos\,}\omega t)``
`` =\frac{\,\mathrm{\,d\,}}{\,\mathrm{\,dt\,}}(A\omega \,\mathrm{\,cos\,}\omega t-B\omega \,\mathrm{\,sin\,}\omega t)``
`` =-A{\omega }^{2}\,\mathrm{\,sin\omega t\,}-B{\omega }^{2}\,\mathrm{\,cos\,}\,\mathrm{\,\omega t\,}``
`` =-{\omega }^{2}(A\,\mathrm{\,sin\,}\omega t+B\,\mathrm{\,cos\,}\omega t)``
`` =-{\omega }^{2}x``
`` ``
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