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Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - NEET MCQ


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10 Questions MCQ Test - Test: Periodic Oscillatory & Simple Harmonic Motion (September 23)

Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) for NEET 2024 is part of NEET preparation. The Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) questions and answers have been prepared according to the NEET exam syllabus.The Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) MCQs are made for NEET 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) below.
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Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 1

A pendulum has time period T for small oscillations. Now, an obstacle is situated below the 
point of suspension O at a distance  The pendulum is released from rest. Throughout the motion, the moving string makes small angle with vertical. Time after which the pendulum returns back to its initial position is

Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 1

For the right (half) oscillation,

For the left (half) oscillation,

Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 2

Three masses of 500 g, 300 g and 100 g are suspended at the end of an ideal  spring as shown and are in equilibrium. When the 500 g mass is suddenly removed, the system oscillated with a period of 2 s. When 300 g mass is also removed, it will oscillate with the period

Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 2

When 500 g is removed, m = (100 + 300)g = 0.4 kg 

When 300 g is also removed, 

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Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 3

A linear harmonic oscillator of force constant 2 x 106 Nm–1 and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?

 

Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 3

Total mechanical energy is 160
ET = J
∴ U max = 160 J

At extreme position KE is zero. Work done by spring force from extreme position to mean position is 

Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 4

A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When the particle passes through the mean position, its KE is 8 ×10-3 J. Find the equation of motion of the particle if the initial phase of oscillation is 45˚

Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 4

Given:
 Mass of the particle, m = 0.1 kg
 Amplitude of SHM, A = 0.1 m
 Kinetic energy at mean position, K.E. = 8×10−3J
 Initial phase of oscillation, ϕ = 45


The kinetic energy at the mean position is given by the formula:
KE = 1/2 mv2
At the mean position, the velocity v is maximum and is given by:
vmax = Aω
Substituting this into the kinetic energy formula gives:
K.E. = 1/2 m (Aω)2


Substituting the known values into the kinetic energy equation:
8×10−3 = 1/2 × 0.1 × (0.1ω)2
This simplifies to:
8 × 10−3 = 0.005 × (0.01ω2)
8 × 10−3 = 5 × 10−5 ω2
Now, solving for ω2:
ω= 8 × 10−3 / 5 × 10−5 = 160
Thus,
ω = √160 = 4 radians/second


The general equation of motion for SHM is given by:
x(t) = A sin(ωt+ϕ)
Substituting the values of A, ω, and ϕ:
Convert ϕ from degrees to radians:
ϕ = 45∘ = π/4 radians
Thus, the equation becomes:
x(t) = 0.1 sin(4t+π/4)



 

Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 5

Two particles executing SHM with same angular frequency and amplitude A and 2A same 
straight line with same position cross other in opposite direction at a distance A/3 from mean position. The phase difference between the two SHM’s is

Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 5

Let particle (1) is moving towards right and particle (2) is moving towards left art this instant, 1 = 0 

Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 6
What is the SI unit of time period (T) in periodic motion?
Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 6
The SI unit of time period (T) in periodic motion is second (s).
Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 7
What is the reciprocal of the time period (T) of periodic motion called?
Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 7
The reciprocal of the time period (T) of periodic motion is called frequency (?).
Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 8
Which type of motion is characterized by a system returning to its equilibrium position after a set of movements?
Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 8
Oscillatory motion is characterized by a system returning to its equilibrium position after a set of movements.
Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 9
What is the mathematical representation of displacement in an oscillatory motion?
Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 9
Displacement in an oscillatory motion can be represented mathematically as f(t) = Acos?t.
Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 10
Which type of motion takes place when the restoring force acting on a system is directly proportional to its displacement from its equilibrium position?
Detailed Solution for Test: Periodic Oscillatory & Simple Harmonic Motion (September 23) - Question 10
Simple harmonic motion takes place when the restoring force acting on a system is directly proportional to its displacement from its equilibrium position.
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