The function x-A sin 2- t-B cos 2- t-C sin- t cos- t represents a simple harmonic motionA- with amplitude - B -2- if A - B and C -28B- with amplitude B -2- if A - B and C -2 BC- for any value of A - B and C- with Q-0D- if A - B and C -0

The correct option is B with amplitude |B/√(2)| if A = B and C = 2Bx = A/2(1 cos 2ω t) + B/2(1+cos 2ω t) +C/2sin 2ω t ...

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Standard XII

Mathematics

Global Maxima

The function ...

Question

The function $x = A s i n^{2} ω t + B c o s^{2} ω t + C s i n ω t c o s ω t$ represents a simple harmonic motion

with amplitude

∣ ∣ \frac{B}{2} ∣ ∣

if A = B and C = 28

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if A = B and C = 0

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with amplitude

∣ ∣ ∣ \frac{B}{\sqrt{2}} ∣ ∣ ∣

if A = - B and C = 2B

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for any value of A, B and C, with C

\neq

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Solution

The correct option is C with amplitude $∣ ∣ ∣ \frac{B}{\sqrt{2}} ∣ ∣ ∣$ if A = - B and C = 2B
$x = \frac{A}{2} (1 - c o s 2 ω t) + \frac{B}{2} (1 + c o s 2 ω t) + \frac{C}{2} s i n 2 ω t$

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Similar questions

x = A {sin}^{2} ω t + B {cos}^{2} ω t + C sin ω t cos ω t

represents SHM -

The displacement x of a particle varies with time t as
$x = A s i n^{2} ω t + B c o s^{2} ω t + C s i n ω t c o s ω t$
For what values of A, B and C is the motion simple harmonic?

When two displacements represented by $y_{1} = a s i n (t)$ and $y_{2} = b c o s (ω t)$ are superimposed the motion is :

Q. The 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

\sqrt{A^{2} + B^{2}} .

Q. A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude
(a) A
(b) B
(c) A + B
(d)

\sqrt{A^{2} + B^{2}} .

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The function x=A sin2 ωt+B cos2 ωt+C sin ωt cos ωt represents a simple harmonic motion

The correct option is C with amplitude ∣∣∣B√2∣∣∣ if A = - B and C = 2Bx=A2(1−cos 2ωt)+B2(1+cos 2ωt)+C2sin 2ωt

The function $x = A s i n^{2} ω t + B c o s^{2} ω t + C s i n ω t c o s ω t$ represents a simple harmonic motion

The correct option is C with amplitude $∣ ∣ ∣ \frac{B}{\sqrt{2}} ∣ ∣ ∣$ if A = - B and C = 2B
$x = \frac{A}{2} (1 - c o s 2 ω t) + \frac{B}{2} (1 + c o s 2 ω t) + \frac{C}{2} s i n 2 ω t$