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A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m?
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A particle is executing SHM about y = 0 along y-axis. Its position at ...
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A particle is executing SHM about y = 0 along y-axis. Its position at ...
Amplitude of SHM
The amplitude of an object in simple harmonic motion (SHM) is defined as the maximum displacement of the object from its equilibrium position. It represents the maximum distance the object can move from its mean position during its oscillation.
Given Information
The position of the particle at an instant is given by y(m) = 5(sin 3πt + √3 cos 3πt)
Finding the Amplitude
To find the amplitude of the particle's motion, we can rewrite the given equation in a standard form for SHM:
y(m) = A sin(ωt + φ)
where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase constant.
Comparing the given equation with the standard form, we can identify the amplitude:
A = 5(1 + √3)
Calculating the Amplitude
To calculate the value of the amplitude, we substitute the given values into the equation:
A = 5(1 + √3)
A = 5 + 5√3
So, the amplitude of the particle's motion is 5 + 5√3 m.
Answer
The amplitude of the particle's oscillation is 5 + 5√3 m.
Explanation
The given equation represents the position of a particle undergoing simple harmonic motion along the y-axis. By comparing the equation with the standard form for SHM, we can determine the amplitude of the particle's motion. Substituting the given values into the equation, we find that the amplitude is 5 + 5√3 m. Therefore, the correct answer is option (3) 5(1 + √3) m.
The amplitude of an object in simple harmonic motion (SHM) is defined as the maximum displacement of the object from its equilibrium position. It represents the maximum distance the object can move from its mean position during its oscillation.
Given Information
The position of the particle at an instant is given by y(m) = 5(sin 3πt + √3 cos 3πt)
Finding the Amplitude
To find the amplitude of the particle's motion, we can rewrite the given equation in a standard form for SHM:
y(m) = A sin(ωt + φ)
where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase constant.
Comparing the given equation with the standard form, we can identify the amplitude:
A = 5(1 + √3)
Calculating the Amplitude
To calculate the value of the amplitude, we substitute the given values into the equation:
A = 5(1 + √3)
A = 5 + 5√3
So, the amplitude of the particle's motion is 5 + 5√3 m.
Answer
The amplitude of the particle's oscillation is 5 + 5√3 m.
Explanation
The given equation represents the position of a particle undergoing simple harmonic motion along the y-axis. By comparing the equation with the standard form for SHM, we can determine the amplitude of the particle's motion. Substituting the given values into the equation, we find that the amplitude is 5 + 5√3 m. Therefore, the correct answer is option (3) 5(1 + √3) m.
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A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m?
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A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m?.
A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is executing SHM about y = 0 along y-axis. Its position at an instant is given by y(m) =5(sin 3πt + √3 cos 3πt). The amplitude of oscillation is:- (1) 10 m (2) 5 m (3) 5(1 + √3) m (4) 5√3 m?.
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