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11th Physics Weekly Test - 3 ( Oscillations )

MABS Institution

11th Physics Weekly Test - 3 ( Oscillations )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

A metal bob is suspended from a coiled spring. When set into vertical vibrations on the earth. It oscillates up 'and down with frequency f. If the same experiment is carried out in a satellite circling the Earth the frequency of vibration will be ________.

f
zero
infinite
depend on the distance of the satellite from the earth

The kinetic energy of a particle, executing SHM, is 16 J when it is at its mean position. If the amplitude of oscillations is 25 cm, and the mass of the particle is 5.12 kg, the time period of its oscillation is _________

\(\pi\)/5 s
2\(\pi\)s
20\(\pi\)s
5\(\pi\)s

A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is

\(T\alpha \frac { 1 }{ { g }^{ 2 }+{ a }^{ 2 } } \)
\(T\alpha \sqrt \frac { 1 }{ { { g }^{ 2 }+{ a }^{ 2 } } } \)
\(T\alpha \sqrt { { g }^{ 2 }+{ a }^{ 2 } } \)
\(\quad T\alpha \left( { g }^{ 2 }+{ a }^{ 2 } \right) \)

What is time period of a pendulum hanged in a satellite? (T is time period on earth)

zero
T
infinite
\(\frac { T }{ \sqrt { 6 } } \)

The motion of a particle is expressed by the equation a = -bx, where x is the displacement from the mean position, a is the acceleration and b is a constant. The periodic time is _______.

\(\frac{2\pi}{b}\)
\(\frac{2\pi}{\sqrt b}\)
2\(\pi \sqrt{2}\)
\(2\sqrt \frac{\pi}{b}\)

The displacement equation of an oscillator is y ==5 sin (0.2 \(\pi\) + 0.5 n) in SI units. The time period of oscillation is ________

10 s
1 s
0.2 s
0.5 s

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm is 4.4 m s^-1. The period of oscillation is

0.01 s
0.1 s
10 s
100 s

The function sin²(ωt) represents

simple harmonic motion with a period π/ω
a simple harmonic motion with a period 2π/ω
a periodic, but not simple harmonic motion with a period π/ω
aperiodic, but not simple harmonic motion with a period 2π/ω

A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system, if a mass 4m is suspended from the same spring?

\(\frac{n}{2}\)
2n
\(\frac{n}{4}\)
4n

The length of a second’s pendulum on the surface of the Earth is 0.9 m. Th e length of the same pendulum on surface of planet X such that the acceleration of the planet X is n times greater than the Earth is

0.9n
\(\frac{0.9}{n}\)m
0.9n²m
\(\frac{0.9}{n^2}\)

The function x =Asin²ωt + B cos²ωt + c sin rot cos rot represents simple harmonic motion for which of the option?

for all values of A, B & C (C# 0) (b) \(\frac{r}{10}\)
A=B, C = 2B
CA = -B, C = 2B
all of the above

When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to \(\frac{1}{3}\)of its initial value. What will be its amplitude when it completes 200 oscillations?.

\(\frac{1}{5}\)
\(\frac{2}{3}\)
\(\frac{1}{6}\)
\(\frac{1}{9}\)

The amplitude of a vibrating body situated in a resisting medium ________.

decreases linearly with time
decreases exponentially with time
decreases with time in some other manner
remains constant with time

A particle executing SHM has an acceleration of 64 cm/s² with its displacement is 4 cm. Its time period, in seconds is ________.

\(\frac{\pi}{2}\)
\(\frac{\pi}{4}\)
\(\pi\)
2\(\pi\)

Two simple harmonic motions act on a particle. These harmonic motions are x = A cos (ωt+&); Y = A cos (ωt + ∝) When &=∝+\(\frac{\pi}{2}\), the resulting motion is _______.

A circle and the actual motion is clockwise
an ellipse and the actual motion is counter clockwise
a ellipse and the actual motion is clockwise
a circle and the actual motion is counter clockwise

The displacement of an object attached to a spring & executing SAM is given by x = 2 x 10^-2 cos πt the time at which the speed first occus is

0.55 μ
0.75 μ
0.125 μ
0.25 μ

Which of the following differential equations represents a damped harmonic oscillator?

\(\frac { { d }^{ 2 }y }{ { dt }^{ 2 } } +y=0\)
\(\frac { { d }^{ 2 }y }{ { dt }^{ 2 } } +\gamma \frac { dy }{ d } +y=0\)
\(\frac { { d }^{ 2 }y }{ { dt }^{ 2 } } +{ k }^{ 2 }+y=0\)
\(\frac { dy }{ d } +y=0\)

Two simple harmonic motions of angular frequencies 100 and 1000 rad/s have the same displacement amplitude. The ratio of their maximum accelerations is _______.

1: 10
1:10²
1:10³
1: 10⁴

A simple harmonic oscillator has amplitude A and time period T. Its maximum speed is ________.

\(\frac{4A}{T}\)
\(\frac{2A}{T}\)
\(\frac{4\pi A}{T}\)
\(\frac{2\pi A}{T}\)

The time period for small vertical oscillations of block of mass m when the masses of the pulleys are negligible and spring constant k₁ and k₂ is

\(T=4\pi \sqrt { m\left( \frac { 1 }{ { k }_{ 1 } } +\frac { 1 }{ { k }_{ 2 } } \right) } \)
\(T=2\pi \sqrt { m\left( \frac { 1 }{ { k }_{ 1 } } +\frac { 1 }{ { k }_{ 2 } } \right) } \)
\(T=4\pi \sqrt { m\left( { k }_{ 1 }+{ k }_{ 2 } \right) } \)
\(T=2\pi \sqrt { m\left( { k }_{ 1 }+{ k }_{ 2 } \right) } \)

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 ________.

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

Find the period of a simple pendulum 1.20 m long.

1.4 s
3.2 s
4.1 s
2.2 s

A particle executing simple harmonic motion has a kinetic energy K_o cos² ωt. The maximum values of the potential energy and the total energy are, respectively ________.

k₀/2 and k₀
k₀ and 2k₀
k₀ and k₀
0 and 2k₀

The total energy of a particle vibrating in SHM is proportional to the square of its _________

velocity
acceleration
amplitude
none of these

A simple pendulum has a time period T₁. When its point of suspension is moved vertically upwards according as y = k t², where y is vertical distance covered and k = 1 ms⁻², its time period becomes T₂. Then, \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \) is (g = 10 m s⁻²)

\(\frac{5}{6}\)
\(\frac{11}{10}\)
\(\frac{6}{5}\)
\(\frac{5}{4}\)

The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minutes will be \(\frac{1}{x}\) time the original, where x is

2 x 3
2³
3²
2x2²

A pendulum is hung in a very high building oscillates to and fro motion freely like a simple harmonic oscillator. If the acceleration of the bob is 16 ms⁻² at a distance of 4 m from the mean position, then the time period is

2 s
1 s
2\(\pi\)s
\(\pi\)s

A particle is executing SHM at mid point of mean position & extermity. What is the potential energy in terms of total energy (E)

\(\frac{E}{4}\)
\(\frac{E}{16}\)
\(\frac{E}{2}\)
\(\frac{C}{8}\)

A body executes SHM with an amplitude A. Its energy is half kinetic and half potential when the displacement is _________

\(\frac{A}{3}\)
\(\frac{A}{2}\)
\(\frac{A}{\sqrt2}\)
\(\frac{A}{2\sqrt2}\)

Masses m_A and m_B hanging from the ends of strings of lengths I_A and I_B are executing. Simple harmonic motions. If their frequencies are related as f_A= 2/_B then ________.

I_A= 2/_B and m_A= m_B/2
I_A = 4/_B regardless of masses
l_A = I_B/4 regardless of masses.
I_A = 2/_B and m_A = 2m_B

A spring is cut into 4-equal parts & 2 parts are connected in parallel. What is the effective in parallel. What is the effective spring contest?

4 k
16 k
8 k
6 k

When a particle oscillates simple harmonically, its potential energy varies periodically. If the frequency of oscillation of the particle is n, the frequency of potential energy variation is _________

\(\frac{n}{3}\)
n
2n
4n

Which one of the following equations of motion represents simple harmonic motion?

Acceleration = - k₀x+ k₁x²
Acceleration = - k(x + a)
Acceleration = k(x + a)
Acceleration = kx

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 phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is ________.

0.5 \(\pi\)
\(\pi\)
0.707 \(\pi\)
zero

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