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6
MCQ (Single Correct Answer)

The displacement of a particle varies with time according to the relation $y=a \sin \omega t+b \cos \omega t$.

A
The motion is oscillatory but not SHM
B
The motion is SHM with amplitude $a+b$
C
The motion is SHM with amplitude $a^2+b^2$
D
The motion is SHM with amplitude $\sqrt{a^2+b^2}$
7
MCQ (Single Correct Answer)

Four pendulums A, B, C and D are suspended from the same

elastic support as shown in figure. $A$ and $C$ are of the same length, while $B$ is smaller than $A$ and $D$ is larger than $A$. If $A$ is given a transerse displacement,

A
$D$ will vibrate with maximum amplitude
B
$C$ will vibrate with maximum amplitude
C
$B$ will vibrate with maximum amplitude
D
All the four will oscillate with equal amplitude
8
MCQ (Single Correct Answer)

Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is

A
$x(t)=B \sin \left(\frac{2 \pi t}{30}\right)$
B
$x(t)=B \cos \left(\frac{\pi t}{15}\right)$
C
$x(t)=B \sin \left(\frac{\pi t}{15}+\frac{\pi}{2}\right)$
D
$x(t)=B \cos \left(\frac{\pi t}{15}+\frac{\pi}{2}\right)$
9
MCQ (Single Correct Answer)

The equation of motion of a particle is $x=a \cos (\alpha t)^2$. The motion is

A
periodic but not oscillatory
B
periodic and oscillatory
C
oscillatory but not periodic
D
neither periodic nor oscillatory
10
MCQ (Single Correct Answer)

A particle executing SHM has a maximum speed of $30 \mathrm{~cm} / \mathrm{s}$ and a maximum acceleration of $60 \mathrm{~cm} / \mathrm{s}^2$. The period of oscillation is

A
$\pi \mathrm{sec}$
B
$\frac{\pi}{2} \mathrm{sec}$
C
$2 \pi \mathrm{sec}$
D
$\frac{\pi}{t} \mathrm{sec}$
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