The displacement of the particle varies with time according to the relation.

$\mathrm{y}=\mathrm{a}<mspace\; width="1em"></mspace>\mathrm{sin\omega t}+\mathrm{b}<mspace\; width="1em"></mspace>\cos <mspace\; width="1em"></mspace>\mathrm{\omega t}$, then

1. The motion is oscillating but not SHM

2. The motion is SHM with amplitude a+b

3. The motion is SHM with amplitude ${\mathrm{a}}^2+{\mathrm{b}}^2$

4. The motion is SHM with amplitude $\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}$

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -

(1) not a simple harmonic

(2) simple harmonic with amplitude a/b

(3) simple harmonic with amplitude $\sqrt{a^{2<mspace\; width="1em"></mspace>}+<mspace\; width="1em"></mspace>b^2}$

(4) simple harmonic with amplitude (a+b)/2

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (\(R/2\)) from the earth's center, where '\(R\)' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
1. \(\frac{2 \pi R}{g} \)
2. \(\frac{\mathrm{g}}{2 \pi \mathrm{R}} \)
3. \(\frac{1}{2 \pi} \sqrt{\frac{g}{R}} \)
4. \(2 \pi \sqrt{\frac{R}{g}} \)

The motion of a particle is given by \(x=A\sin\omega t+B\cos\omega t\). The motion of the particle is:

When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -

1. not a simple harmonic

2. simple harmonic with amplitude a/b

3. simple harmonic with amplitude $\sqrt{a^{2<mspace\; width="1em"></mspace>}+<mspace\; width="1em"></mspace>b^2}$

4. simple harmonic with amplitude (a+b)/2

The displacement equation of a particle is $x=3\sin <mspace\; width="1em"></mspace>2t+4\cos <mspace\; width="1em"></mspace>2t<mspace\; width="1em"></mspace>$ The amplitude and maximum velocity will be respectively

(a)       5, 10       (b)         3, 2

c)         4, 2        (d)         3, 4