SHM as projection of circular motion - class-XI

Question 1 Multiple Choice (Single Answer)

Two SHMs are represented by the equations
$y1=10sin(3\Omega t+\frac{\Omega }{4})$ and
$y2=5[sin3\Omega t+\sqrt{3}cos 3\Omega t]$. their amplitudes and in the ratio

1:2
2:1
1:3
1:1

Question 2 Multiple Choice (Single Answer)

A simple harmonic oscillator starts from extreme position and covers a displacement half of its amplitude in a time '$t$', the further time taken by it to reach mean position is

$2t$
$t$
$ t/\sqrt{2} $
$t/2$

Question 3 Multiple Choice (Single Answer)

The circular motion of a particle whose speed is constant is

Periodic but not simple harmonic
Simple harmonic but not periodic
Periodic and simple harmonic
Neither periodic not simple harmonic

Question 4 Multiple Choice (Single Answer)

Find the distance covered by a particle from time $t=0$ to $t=6\ \sec$. When the particle followsa the movement in straight line according to $y=a\cos \left(\dfrac {\pi}{4}\right)t$:-

$a$
$2a$
$3a$
$4a$

Question 5 Multiple Choice (Single Answer)

The particle executes SHM on a straight line. At two positions its velocity $u$ and $v$ while acceleration, $\alpha$ and $\beta$ respectively $[\beta > \alpha >0]$, the distance between the two positions will be:-

$\dfrac{u^2+v^2}{\alpha+\beta}$
$-\dfrac{u^2-v^2}{\alpha+\beta}$
$\dfrac{u^2-v^2}{\alpha-\beta}$
$\dfrac{u^2+v^2}{\beta-\alpha}$

Question 6 Multiple Choice (Single Answer)

To understand Simple Harmonic Motion as analogous to circular motion,

we project the circular motion of the particle along any radius.
we project the circulation motion of the particle along a chord.
we project the circulation motion of the particle along the diameter.
None of these.

Question 7 Multiple Choice (Single Answer)

The actual distance moved along the circle will be the distance moved by the projection on the diameter.

less than
equal to
greater than
None of these

Question 8 Multiple Choice (Single Answer)

The particle executes SHM on a straight line. At two positions its velocity $u$ and $v$ while acceleration, $\alpha$ and $\beta$ respectively $[\beta > \alpha >0]$, the distance between the two positions will be:-

$\frac{u^2+v^2}{\alpha+\beta}$
$-\frac{u^2-v^2}{\alpha+\beta}$
$\frac{u^2-v^2}{\alpha-\beta}$
$\frac{u^2+v^2}{\beta-\alpha}$

Question 9 Multiple Choice (Single Answer)

The period of a particle it is $8s$. At $t=0$ it is at the mean position. The ratio of the distance covered by the particle in first second and second will be

$\cfrac { \sqrt { 2 } -1 }{ \sqrt { 2 } } $
$\cfrac { 1 }{ \sqrt { 2 } } $
$\cfrac { 1 }{ \sqrt { 2 } -1 } $
$\left[ \sqrt { 2 } -1 \right] $

Question 10 Multiple Choice (Single Answer)

Simple harmonic motion is the projection of uniform circular motion on the

$x$- axis
$y$- axis
reference circle
any diameter of reference circle.

SHM as projection of circular motion - class-XI

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