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11th Physics Weekly Test - 1 ( Oscillations )

MABS Institution

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

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

A body is executing simple harmonic motion with an angular frequency 2 rod/sec. The velocity of the body at 20mm displacement, when the amplitude of motion is 60mm, is

90 mm/s
113 mm/s
118 mm/s
131 mm/s

A particle executing simple harmonic motion along y-axis has its motion described by the equation y = A.sin (ωt) + B, the amplitude of the example harmonic motion is

A
B
A+B
\(\sqrt{A+B}\)

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 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

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

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

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

A loaded spring vibrates with a period T. The spring is divided into four equal parts and the same load is suspended from one as these parts. The new time period is _______

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

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

Part - B

Generic 2 - Answer All Question

Which of the following functions of time represent periodic and non-periodic motion?
a. sin ωt + cos ωt
b. ln ωt

The acceleration dual to gravity on the surface of moon is 1.7 ms^-2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s?

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

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/3. What is the ratio m/M?

Part - C

Generic 3 - Answer All Question

What will be the change in time period of a loaded spring, when taken to moon?

A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5 m s⁻¹. Suppose a body of mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.

Can a motion be oscillatory, but not simple hormonic. If your answer is yes, give an explanation and if not explain why?
The body of a bus begins to rattle sometimes, when the bus picks up a certain speed, why?

Derive the expression for resultant spring constant when two springs having constant k_land k₂ are connected in series.

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

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

Show that for a simple harmonic motion, the phase difference between
a. displacement and velocity is \(\frac{\pi}{2}\)radian or 90°.
b. velocity and acceleration is \(\frac{\pi}{2}\)radian or 90°.
c. displacement and acceleration is \(\pi\) radian or 180°.

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)
Explain in detail the four different types of oscillations.

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