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An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm
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An object perform S. H. M. of amplitude 5cm and time period 4s. If tim...
Answer:
Given:
Amplitude, A = 5cm
Time period, T = 4s
Initial displacement, x = 0
I) Frequency of oscillation:
Frequency of oscillation, f = 1/T
f = 1/4s
f = 0.25Hz
Therefore, the frequency of oscillation is 0.25Hz.
II) Displacement at 0.5s:
The displacement of the object at any given time t can be given by the equation:
x = A sin(2πft)
where A is the amplitude, f is the frequency, and t is the time.
Given that the object is at the center of the oscillation, IE, x = 0
Thus, the equation becomes:
0 = A sin(2πft)
sin(2πft) = 0
This means that the object is at the center of the oscillation at t = 0, T/2, 2T/2, 3T/2, etc.
At t = 0.5s, the object is at the extreme position, so
x = A sin(2πft)
x = 5cm sin(2π x 0.25Hz x 0.5s)
x = 5cm sin(π)
x = 0
Therefore, the displacement of the object at 0.5s is 0cm.
III) Maximum acceleration of the object:
The acceleration of the object at any given time t can be given by the equation:
a = -Aω^2sin(ωt)
where A is the amplitude, ω is the angular frequency, and t is the time.
Angular frequency, ω = 2πf
ω = 2π x 0.25Hz
ω = 1.57rad/s
At the extreme position, x = A, so
a = -Aω^2
a = -5cm x (1.57rad/s)^2
a = -12.4cm/s^2
The maximum acceleration of the object is 12.4cm/s^2.
IV) Velocity at a displacement of 3cm:
The velocity of the object at any given time t can be given by the equation:
v = -Aωcos(ωt)
where A is the amplitude, ω is the angular frequency, and t is the time.
Angular frequency, ω = 2πf
ω = 2π x 0.25Hz
ω = 1.57rad/s
At x = 3cm, the equation becomes:
3cm = 5cm sin(ωt)
sin(ωt) = 0.6
ωt = sin^-1(0.6)
ωt = 0.64 rad
At t = 0.41s, the object is at x = 3cm
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An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm
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An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm.
An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm.
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An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm, a detailed solution for An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm has been provided alongside types of An object perform S. H. M. of amplitude 5cm and time period 4s. If timing is started when the object is at the center of the oscillation IE, x=0then calculate. (I) frequency of oscillation (II) the displacement at 0.5s (III) the maximum acceleration of the object. (4)the velocity at a displacement of 3cm theory, EduRev gives you an
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