Function `x=Asin^(2)omegat+Bcos^(2)omegat+Csinomegat cos omegat` represents simple harmonic motion,
A
The motion of particle is `SHM` when `A = B`
B
The motion of particle is `SHM` when `A = B` and `C = 0`
C
If `B = C/2=-A`, then the amplitude of `SHM` is `B//sqrt(2)`.
D
If `A=B =C/2`, then the axis of vibration of `SHM` shifts by a distance `B` towards `+x` axis.
Text Solution
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The correct Answer is:
ACD
If ` A = B` then `x = A + C sinomegat cosomegat = A + C/2 sin^(2)omegat rArr "SHM"` If `A = B` & `C = 0` then `x = A rArr ` along a straight line. If `B = C/2 = - A` then `x = B cos^(2)omegat + Bsin2omegat rArr "amplitude" = Bsqrt(2)` If `A = B= C/2` then `x = B + Bsin2omegat rArr` Axis of vibration of SHM shifts by a distance B towards `+ x-` axis.
Function x=Asin^2omegat+Bcos^2omegat+Csinomegatcosomegat represents SHM (i) For any value of A, B and C(except C=0 ) (ii) If A=-B , C=2B , amplitude =|Bsqrt2| (iii) If A=B , C=0 (iv) If A=B , C=2B , amplitude =|B|
Show that a linear combination of sine and cosine function like x(t)=a sin omegat+b cos omegat represents a simple harmonic. Also, determine its amplitude and phase constant.
What is the time period for the function f(t) = sin omegat + cos omega t may represent the simple harmonic motion ?
