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Wave Equation

A particle wi...

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A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinwt . If the amplitude of the particle is maximum for w=w1 and energy of the particle is maximum for w=w2 ,then (where w° is natural frequency of oscillation of particle) (a)w1=w° and w2not=w° (b)w1=w° & w2=w° (c) w1 not=w° & w2=w° (d)w1not=w° & w2 not=w°

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Q. If W1, W2 and W3 represents the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3.

Q. A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force

F s i n ω .

If the amplitude of the particle is maximum for

ω = ω_{1}

and the energy of the particle is maximum for

ω = ω_{2}

ω_{0}

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1, w, w^{2}

are three cube roots of unity, then

(1 - w + w^{2}) (1 + w - w^{2})

If 1, w, $w^{2}$ are three cube roots of unity, then $(1 - w + w^{2}) (1 + w - w^{2})$ is .............

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