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Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2?
Most Upvoted Answer
Particle moves in a straight line, with simple harmonic motion, making...
Solution:
Given, number of oscillations, n = 7 and time period, T = 11 sec.
Hence, time period of one oscillation, t = T/n = 11/7 sec.
Velocity of the particle, v = 1.2 m/sec and distance from the centre of oscillation, x = 12.5 cm.
Amplitude:
Let A be the amplitude of the motion.
The displacement of the particle from the centre of oscillation can be given by
x = A sin(2πt/T)
Putting the given values, we get
0.125 = A sin(2π(11/7)/T)
0.125 = A sin(2π/7)
A = 0.125/sin(2π/7)
A ≈ 0.325 m or 32.5 cm
Hence, the amplitude of the motion is 32.5 cm.
Maximum velocity:
The maximum velocity of the particle can be given by
v_max = Aω
where ω = 2π/T is the angular frequency of the motion.
Putting the given values, we get
v_max = 0.325 × 2π/(11/7)
v_max ≈ 1.3 m/sec
Hence, the maximum velocity of the particle is 1.3 m/sec.
Maximum acceleration:
The acceleration of the particle can be given by
a = -Aω^2 sin(2πt/T)
The maximum value of sin function is 1, hence the maximum acceleration is
a_max = Aω^2
Putting the given values, we get
a_max = 0.325 × (2π/(11/7))^2
a_max ≈ 5.2 m/sec^2
Hence, the maximum acceleration of the particle is 5.2 m/sec^2.
Therefore, the correct option is (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec^2.
Given, number of oscillations, n = 7 and time period, T = 11 sec.
Hence, time period of one oscillation, t = T/n = 11/7 sec.
Velocity of the particle, v = 1.2 m/sec and distance from the centre of oscillation, x = 12.5 cm.
Amplitude:
Let A be the amplitude of the motion.
The displacement of the particle from the centre of oscillation can be given by
x = A sin(2πt/T)
Putting the given values, we get
0.125 = A sin(2π(11/7)/T)
0.125 = A sin(2π/7)
A = 0.125/sin(2π/7)
A ≈ 0.325 m or 32.5 cm
Hence, the amplitude of the motion is 32.5 cm.
Maximum velocity:
The maximum velocity of the particle can be given by
v_max = Aω
where ω = 2π/T is the angular frequency of the motion.
Putting the given values, we get
v_max = 0.325 × 2π/(11/7)
v_max ≈ 1.3 m/sec
Hence, the maximum velocity of the particle is 1.3 m/sec.
Maximum acceleration:
The acceleration of the particle can be given by
a = -Aω^2 sin(2πt/T)
The maximum value of sin function is 1, hence the maximum acceleration is
a_max = Aω^2
Putting the given values, we get
a_max = 0.325 × (2π/(11/7))^2
a_max ≈ 5.2 m/sec^2
Hence, the maximum acceleration of the particle is 5.2 m/sec^2.
Therefore, the correct option is (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec^2.
Community Answer
Particle moves in a straight line, with simple harmonic motion, making...
Option (1) is correct.
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Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2?
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Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2?.
Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2?.
Solutions for Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? in English & in Hindi are available as part of our courses for NEET.
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Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2?, a detailed solution for Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? has been provided alongside types of Particle moves in a straight line, with simple harmonic motion, making seven complete oscillations in 11 sec. The velocity of the particle is 1.2 m/sec, when its distance from the centre of oscillation is 12.5 cm. Find the amplitude of the motion, the maximum velocity and maximum acceleration: (1) 32.5 cm, 1.3 m/sec, 5.2 m/sec2 (2) 20 cm, 26 m/sec, 10.4 m/sec2 (3) 2.5 cm, 13 m/sec, 5.2 m/sec2 (4)32.5 cm, 10 m/sec, 15.2 m/sec2? theory, EduRev gives you an
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