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11th Physics Monthly Test - 2 ( Oscillations )

MABS Institution

11th Physics Monthly Test - 2 ( Oscillations )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

The phase difference between the unstantaneous velocity & acceleration of a particle executing simple harmonic motion is

0.5 π
π
0.707π
0.61 m

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

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

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 pendulum 1.20 m long is observer to have 1 m Long is observed to have a period of 2.00 s at a certain location then the acceleration due to gravity is,

9.71 m/s²
9.85 m/s²
9.79 m/s²
10.1 m/s²

Which of the following function represents a simple harmonic oscellation?

sin ωt - cos ωt
sinωt+sin2ωt
sinωt-sin2ωt
sin²ωt

Two simple pendulums of lengths 0.5m and 2.0m respectively are given small linear displacement in one direction at the same time. They will again be in phase when the pendulum of shorter length has completed _______ oscillations.

5
3
1
2

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during' the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is _________.

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

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

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

Part - B

Generic 2 - Answer All Question

Write short notes on two springs connected in parallel.

Define molar specific heat capacity.

An oscillating block-spring system has a mechanical energy of 1.00 J, an amplitude of 10.0 cm and a maximum speeding of 1.20 m/s. Find the spring constant, the mass of the block, and the frequency of oscillation.
Define velocity in SHM.

A mass m moves with a speed v on a horizontal smooth surface and collides with a nearly massless spring whose spring constant is k. If the mass stops after collision, compute the maximum compression of the spring.

Define forced oscillation. Give an example.

Define Amplitude.

Part - C

Generic 3 - Answer All Question

A nurse measured the average heart beats of a patient and reported to the doctor in terms of time period as 0.8 s. Express the heart beat of the patient in terms of number of beats measured per minute.

A body oscillates with SHM along with x-axis. Its displacement varies with time according to the equation x = (4.00 m) cos (\({ \pi }_{ t }^{ + }\frac { \pi }{ 4 } \)) calculate at t = 1.00 s: (a) displacement (b) velocity (c) acceleration (d) Also calculate the maximum speed and maximum acceleration and (e) phase at t = 2.00 s.

Will a pendulum clock lose or gain time when taken to the top of a mountain?

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 can earthquakes cause disaster sometimes?

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

Part - D

Generic 5 - Answer All Question

Explain Displacement, velocity in SHM, and derive special cases.

Write down the difference between simple harmonic motion and angular simple harmonic motion.

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

Discuss in detail the energy in simple harmonic motion.

What is meant by angular harmonic oscillation? Compute the time period of angular harmonic oscillation.

Show that for a particle executing simple harmonic motion
a. the average value of kinetic energy is equal to the average value of potential energy.
b. average potential energy = average
kinetic energy =\(\frac{1}{2}\)(total energy)
Hint : average kinetic energy = <energy> \(=\frac { 1 }{ T } \int _{ 0 }^{ T}{ } \)(Kinetic energy)dt and average potential energy = <Potential energy> \(=\frac { 1 }{ T } \int _{ 0 }^{ T}{ } \)(Potential energy)dt

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the liquid column of mercury in the U-tube executes simple harmonic motion.

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