Oscillations Test

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Oscillations Test - 79

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Question 1
1 / -0

A particle moves in x-y plane according to the equation $$\overrightarrow {r } =(\hat { i } +2\hat { j })$$ $$A\, cos \,\omega t$$. The motion of the particle is

A
simple harmonic

B
uniformly accelerated

C
circular motion

D
projectile motion

Solution
Question 2
1 / -0

A particles moves on the x-axis according to the equation $${ x=x }_{ 0 }{ sin }^{ 2 }\omega t$$. The motion is simple harmonic

A
With amplitude $${ x }_{ 0 }$$

B
With amplitude $${ 2x }_{ 0 }$$

C
With time period $$\dfrac { 2\pi }{ \omega } $$

D
With time period $$\dfrac { \pi }{ \omega } $$

Solution
Question 3
1 / -0

Periodic and Oscillatory Motions, Period and Frequency, Displacement
Identify the correct definition

A
If after every certain interval of time, particle repeats its motion then motion is called periodic motion

B
To and fro motion of a particle over the same path is called oscillatory motion

C
Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion

D
All of these

Solution
Question 4
1 / -0

A particle executes SHM in accordance with x = A sin $$\omega t.$$ If $${ t }_{ 1 }$$ is the time taken by it to reach from x = 0 to x = $$\sqrt { 3 } (A/2)$$ and $${ t }_{ 2 }$$ is the time taken by it to reach from x = $$\left( \sqrt { 3 } /2 \right) A$$ to x = A the value of $${ t }_{ 1 }/{ t }_{ 2 }$$ is

A
2

B
$$\dfrac { 1 }{ 2 } $$

C
3

D
$$\dfrac { 1 }{ 3 } $$

Solution
Question 5
1 / -0

The value of phase at maximum displacement from the mean position of a particle in S.H.M. is

A
$$\pi /2$$

B
$$\pi $$

C
Zero

D
$$2\pi $$

Solution
Question 6
1 / -0

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?

A
$$ Y = a sin 2 \pi t/ T - cos 2 \pi t / T $$

B
Y = a sin Vt

C
$$ y = \dfrac {a}{T} sin \left( \dfrac { Kt }{ a } \right) $$

D
$$ Y\quad =\quad a\sqrt { 2 } \left( sin\dfrac { 2\pi t }{ T } -cos\dfrac { 2\pi t }{ T } \right) $$

Solution
Question 7
1 / -0

A block of mass $$1 kg$$ is connected with a massless spring of force constant $$100 N/m$$. At $$t=0$$, a constant force $$F=10 N$$ is applied on the block. The spring is in its natural length at $$t=0$$. The speed of particle at $$x=6cm$$ from mean position is:

A
$$4 cm/s$$

B
$$10 cm/s$$

C
$$80 cm/s$$

D
$$50 cm/s$$

Solution
Question 8
1 / -0

Potential energy of a particle of mass is given by $$U\quad =-\quad { U }_{ 0 }\left( 1-\cos {a x } \right) .$$ which of the following can be a possible expression for its time period

A
$$2\pi \sqrt { \frac { m }{ { a }^{ 2 }{ u }_{ 0 } } } $$

B
$$2\pi \sqrt { \frac { m }{ { a }{ u }_{ 0 } } } $$

C
$$2\pi \sqrt { \frac { ma }{ { U }_{ 0 } } } $$

D
$$2\pi \sqrt { \frac { { mu }_{ 0 } }{ a } } $$

Solution
Question 9
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A particle executing SHM has max acceleration $$ 50 cm/s^2 $$ , The time period of oscillation of 2 sec and initial displacement 2.5 cm from the equilibrium position.The equation of SHM is $$ (take\ \pi^2 = 10) $$

A
$$ X = 2.5 sin \left( \pi t + \frac { \pi }{ 6 } \right) cm $$

B
$$ X = 5 sin \left( \frac { \pi t }{ 2 } +\frac { \pi }{ 3 } \right) cm $$

C
$$ X = 5 sin \left( \pi t+\frac { \pi }{ 3 } \right) cm$$

D
$$X = 5 sin \left( \pi t+\frac { \pi }{ 6 } \right) cm $$

Solution
Question 10
1 / -0

The equation of an SHM with amplitude $$A$$ and angular frequency $$\omega$$ in which all the distances are measured from one extreme position and time is taken to be zero at the other extreme position is

A
$$x = A \sin \omega t$$

B
$$x = A (\cos \omega t + \sin \omega t)$$

C
$$x = A - A \cos \omega t$$

D
$$x = A + A \cos \omega t$$

Solution

From given question
$$t = 0$$
$$x = 2A$$
Put $$t = 0, x$$ should be $$2A$$
I) $$x = A\sin 0 = 0 \ X$$
II) $$x = A(\cos 0 + \sin 0) = A \ X$$
III) $$x = A - A\cos 0 = 0 \ X$$
IV) $$X = A + A\cos 0 = A + A = 2A \checkmark$$