11th Physics Monthly Test - 1 ( Oscillations )

MABS Institution

11th Physics Monthly Test - 1 ( Oscillations )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

In forced oscillations of a particle, the amplitude is maximum for a frequency wI of the force, while the energy is maximum for a frequency ω₂ of the force. Then _______.

ω₁<ω₂
ω₁<ω₂when damping is small and ω₁>ω₂ when damping is large_.
ω₁>ω₂
ω₁=ω₂

In order to double the period of a simple pendulum _______.

its length should doubled
its length should be quadrupled
the mass of its bob should be doubled
the mass of its bob should be quadrupled.

A massless spring, having force constant k, oscillates with a frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is suspended from one of the parts. The frequency of oscillation will now be _______

n
\(n\sqrt{2}\)
\(\frac{n}{\sqrt 2}\)
2 n

The angular velocity and the amplitude of a simple pendulum are co and a, respectively. The ratio of its kinetic and potential energies at a displacement x from the mean position is ________.

\(\frac { { x }^{ 2 }{ \omega }^{ 2 } }{ { a }^{ 2 }-{ x }^{ 2 }{ \omega }^{ 2 } } \)
\(\frac { { x }^{ 2 } }{ { a }^{ 2 }-{ x }^{ 2 } } \)
\(\frac { { { a }^{ 2 }-x }^{ 2 }{ \omega }^{ 2 } }{ { x }^{ 2 }{ \omega }^{ 2 } } \)
\(\frac { { a }^{ 2 }-{ x }^{ 2 } }{ { x }^{ 2 } } \)

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is Vex) = kx₂ .Where k is a positive constant. If the amplitude of oscillation is a, then its time period T is ________.

Proportional to \(\frac{1}{\sqrt{a}}\)
independent of a
proportional to \(\sqrt{a}\)
proportional to a^3/2

The three springs with force constant \({ k }_{ 1 }=7.5\frac { N }{ m } ,{ k }_{ 2 }=10.0\frac { N }{ m } ,{ k }_{ 3 }=12.5\frac { N }{ m } \), are connected in parallel to a mass of 0.500 kg. The mass is then pulled to the right and released. Then the period of the motion is.

0.6s
0.8s
0.5 s
0.4 s

A particle executing simple harmonic motion of amplitude 5 em has maximum speed of 31.4 cm/s. The frequency of its oscillation is _______

3 Hz
4 Hz
2 Hz
1 Hz

A girl is swinging on a swing in the sitting position. How will the period of swing be affected if she stands up?

The period will now he shorter
The period will now be longer
The period win remain unchanged
The period may become longer or shorter depending upon the height of the girl

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m.1f the piston moves with S.H.M with an angular frequency of 200 rad/min. Then the maximum speed will be,

50 m/min
100m/min
150m/min
200 m/min

Two bodies A and B whose masses are in the ratio 1:2 are suspended from two separate massless springs of force constants kA and kB respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is

\(\sqrt { \frac { { K }_{ B } }{ { 2 }K_{ A } } } \)
\(\sqrt { \frac { { K }_{ B } }{ { 8 }K_{ A } } } \)
\(\sqrt { \frac { {2 K }_{ B } }{ { }K_{ A } } } \)
\(\sqrt { \frac { {8 K }_{ B } }{ { }K_{ A } } } \)

Part - B

Generic 2 - Answer All Question

What is meant by maintained oscillation?. Give an example.

Explain resonance. Give an example.

Calculate the time period of the oscillation of a particle of mass m moving in the potential defined as
U(x)={\(\frac { 1 }{ 2 } k{ x }^{ 2 },x<0\\ mgx,x>0\)

Compute the time period for the following system if the block of mass m is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.
Consider two simple harmonic motion along x and y-axis having same frequencies but different amplitudes as x = A sin (\(\omega t+\psi \)) (along x axis) and y = B sin ωt (along y axis). Then show that
\(\frac { { x }^{ 2 } }{ { A }^{ 2 } } +\frac { { y }^{ 2 } }{ { B }^{ 2 } } -\frac { 2xy }{ AB } cos\psi =sin^{ 2 }\psi \)
and also discuss the special cases when
a.\(\psi =0\) \(b.\psi =\pi \) \(c.\psi =\frac { \pi }{ 2 } \)
\(d.\psi =\frac { \pi }{ 2 } and\quad A=B\)\(e.\psi =\frac { \pi }{ 4 } \)
Note: when a particle is subjected to two simple harmonic motion at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures.

Consider two springs whose force constants are 1 N m⁻¹and 2 N m⁻¹ which are connected in series. Calculate the effective spring constant (k_s) and comment on k_s.

What is meant by free oscillation?

Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.

What is meant by angular oscillation?

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum oscillator. The acceleration of the bob of the pendulum is 20 ms-2 at a distance of 5 m from the mean position. To find the time period of oscillation.

Part - C

Generic 3 - Answer All Question

Glass windows may be broken by a far away explosion. Explain why?

A particle moving in a straight line has velocity v given by v² = a - \(\beta\)y², where a and P are constant and y is its distance from a fixed point in the line. Show that the motion of the particle is SHM. Find its time period and amplitude.

Sometimes a wire glass is broken by the powerful voice of a celebrated singer why?

Why are army troops not allowed to march in steps while crossing the ridge?

Every simple harmonic motion is periodic motion but every periodic motion need not be simple harmonic motion. Do you agree? Give example.

If the length of the simple pendulum is increased by 44% from its original length, calculate the percentage increase in time period of the pendulum.
Consider two springs with force constants 1 N m⁻¹ and 2 N m⁻¹ connected in parallel. Calculate the effective spring constant (k_p) and comment on k_p.

A uniform disk of radius r = 0.6 m and mass M = 2.5 kg is freely suspended from a horizontal pivot located a radial distance d = 0.30 m from its centre. Find the angular frequency of small amplitude oscillations of the disk.

A particle executes SHM with a time period of 16 s. At time t = 2 s, the particle crosses the mean position while at t = 4 s, its velocity is 4 ms^-1, Find its amplitude of motion.

How would the time period of a spring mass system change, when it is made to oscillate horizontally and then vertically?

Part - D

Generic 5 - Answer All Question

Which of the following represent simple
harmonic motion?
(i) x = A sin ωt + B cos ωt
(ii) x = A sin ωt+ B cos 2ωt
(iii) x = A e^iωt
(iv) x = A ln ωt

Consider a particle undergoing simple harmonic motion. The velocity of the particle at position x₁ is v₁ and velocity of the particle at position x₂is v₂. Show that the ratio of time period and amplitude is
\(\frac { T }{ A } =2\pi \sqrt { \frac { { x }_{ 2 }^{ 2 }-{ x }_{ 1 }^{ 2 } }{ { { v }_{ 1 }^{ 2 }x }_{ 2 }^{ 2 }-{ { v }_{ 2 }^{ 2 }x }_{ 1 }^{ 2 } } } \)

Explain briefly about the graphical representation of Displacement, velocity and acceleration in SHM.

Two simple harmonic moles are represented by Y₁=0.1 sin (100 \(\pi\)t + \(\pi\)/3) and Y₂=0.1 cos rtt what is the phase difference of the velocity of the particle 1 with respect to the velocity of particle?

Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below
a. y = 0.3 sin (40\(\pi\)t + 1.1)
b. y = 2 cos (\(\pi\)t)
c. y = 3 sin (2\(\pi\)t − 1.5)

Show that the projection of uniform circular motion on a diameter is SHM.

Discuss the simple pendulum in detail.
Write a short note on Simple Harmonic Motion.

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple. Pendulum depends on its length (I), mass of the bob, (m) und acceleration due to gravity ,(g). Derive the expression for its time period using method of dimension.

In simple pendulum experiment, we have used small angle approximation. Discuss the small angle approximation.

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11th Physics Monthly Test - 1 ( Oscillations )

MABS Institution

11th Physics Monthly Test - 1 ( Oscillations )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

In forced oscillations of a particle, the amplitude is maximum for a frequency wI of the force, while the energy is maximum for a frequency ω2 of the force. Then _______.

In order to double the period of a simple pendulum _______.

A massless spring, having force constant k, oscillates with a frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is suspended from one of the parts. The frequency of oscillation will now be _______

The angular velocity and the amplitude of a simple pendulum are co and a, respectively. The ratio of its kinetic and potential energies at a displacement x from the mean position is ________.

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is Vex) = kx2 .Where k is a positive constant. If the amplitude of oscillation is a, then its time period T is ________.

The three springs with force constant \({ k }_{ 1 }=7.5\frac { N }{ m } ,{ k }_{ 2 }=10.0\frac { N }{ m } ,{ k }_{ 3 }=12.5\frac { N }{ m } \), are connected in parallel to a mass of 0.500 kg. The mass is then pulled to the right and released. Then the period of the motion is.

A particle executing simple harmonic motion of amplitude 5 em has maximum speed of 31.4 cm/s. The frequency of its oscillation is _______

A girl is swinging on a swing in the sitting position. How will the period of swing be affected if she stands up?

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m.1f the piston moves with S.H.M with an angular frequency of 200 rad/min. Then the maximum speed will be,

Two bodies A and B whose masses are in the ratio 1:2 are suspended from two separate massless springs of force constants kA and kB respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio 1:2, the ratio of the amplitude A to that of B is

Part - B

Generic 2 - Answer All Question

What is meant by maintained oscillation?. Give an example.

Explain resonance. Give an example.

Calculate the time period of the oscillation of a particle of mass m moving in the potential defined as U(x)={\(\frac { 1 }{ 2 } k{ x }^{ 2 },x<0\\ mgx,x>0\)

Compute the time period for the following system if the block of mass m is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.

Consider two springs whose force constants are 1 N m−1 and 2 N m−1 which are connected in series. Calculate the effective spring constant (ks) and comment on ks.

What is meant by free oscillation?

Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.

What is meant by angular oscillation?

Part - C

Generic 3 - Answer All Question

Glass windows may be broken by a far away explosion. Explain why?

A particle moving in a straight line has velocity v given by v2 = a - \(\beta\)y2, where a and P are constant and y is its distance from a fixed point in the line. Show that the motion of the particle is SHM. Find its time period and amplitude.

Sometimes a wire glass is broken by the powerful voice of a celebrated singer why?

Why are army troops not allowed to march in steps while crossing the ridge?

Every simple harmonic motion is periodic motion but every periodic motion need not be simple harmonic motion. Do you agree? Give example.

If the length of the simple pendulum is increased by 44% from its original length, calculate the percentage increase in time period of the pendulum.

Consider two springs with force constants 1 N m−1 and 2 N m−1 connected in parallel. Calculate the effective spring constant (kp) and comment on kp.

A uniform disk of radius r = 0.6 m and mass M = 2.5 kg is freely suspended from a horizontal pivot located a radial distance d = 0.30 m from its centre. Find the angular frequency of small amplitude oscillations of the disk.

A particle executes SHM with a time period of 16 s. At time t = 2 s, the particle crosses the mean position while at t = 4 s, its velocity is 4 ms-1, Find its amplitude of motion.

How would the time period of a spring mass system change, when it is made to oscillate horizontally and then vertically?

Part - D

Generic 5 - Answer All Question

Which of the following represent simple harmonic motion? (i) x = A sin ωt + B cos ωt (ii) x = A sin ωt+ B cos 2ωt (iii) x = A eiωt (iv) x = A ln ωt

Explain briefly about the graphical representation of Displacement, velocity and acceleration in SHM.

Two simple harmonic moles are represented by Y1=0.1 sin (100 \(\pi\)t + \(\pi\)/3) and Y2=0.1 cos rtt what is the phase difference of the velocity of the particle 1 with respect to the velocity of particle?

Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below a. y = 0.3 sin (40\(\pi\)t + 1.1) b. y = 2 cos (\(\pi\)t) c. y = 3 sin (2\(\pi\)t − 1.5)

Show that the projection of uniform circular motion on a diameter is SHM.

Discuss the simple pendulum in detail.

Write a short note on Simple Harmonic Motion.

In simple pendulum experiment, we have used small angle approximation. Discuss the small angle approximation.

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In forced oscillations of a particle, the amplitude is maximum for a frequency wI of the force, while the energy is maximum for a frequency ω₂ of the force. Then _______.

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is Vex) = kx₂ .Where k is a positive constant. If the amplitude of oscillation is a, then its time period T is ________.

Calculate the time period of the oscillation of a particle of mass m moving in the potential defined as
U(x)={\(\frac { 1 }{ 2 } k{ x }^{ 2 },x<0\\ mgx,x>0\)

Consider two springs whose force constants are 1 N m⁻¹and 2 N m⁻¹ which are connected in series. Calculate the effective spring constant (k_s) and comment on k_s.

A particle moving in a straight line has velocity v given by v² = a - \(\beta\)y², where a and P are constant and y is its distance from a fixed point in the line. Show that the motion of the particle is SHM. Find its time period and amplitude.

Consider two springs with force constants 1 N m⁻¹ and 2 N m⁻¹ connected in parallel. Calculate the effective spring constant (k_p) and comment on k_p.

A particle executes SHM with a time period of 16 s. At time t = 2 s, the particle crosses the mean position while at t = 4 s, its velocity is 4 ms^-1, Find its amplitude of motion.

Which of the following represent simple
harmonic motion?
(i) x = A sin ωt + B cos ωt
(ii) x = A sin ωt+ B cos 2ωt
(iii) x = A e^iωt
(iv) x = A ln ωt

Two simple harmonic moles are represented by Y₁=0.1 sin (100 \(\pi\)t + \(\pi\)/3) and Y₂=0.1 cos rtt what is the phase difference of the velocity of the particle 1 with respect to the velocity of particle?

Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below
a. y = 0.3 sin (40\(\pi\)t + 1.1)
b. y = 2 cos (\(\pi\)t)
c. y = 3 sin (2\(\pi\)t − 1.5)