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Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.?
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Two masses A & B each of 5 kg are suspended by a light inextensible st...
And B are connected by a spring. Mass A has a mass of 2 kg and is attached to the spring, while mass B has a mass of 3 kg and is free to move. The spring has a spring constant of 5 N/m.
a) Calculate the natural frequency of the system.
The natural frequency of the system can be calculated using the formula:
f = 1/(2π) * √(k/m)
where f is the natural frequency, k is the spring constant, and m is the equivalent mass of the system.
The equivalent mass of the system can be calculated as:
m = m1 + m2
where m1 is the mass of mass A and m2 is the mass of mass B.
m = 2 kg + 3 kg = 5 kg
Substituting the values in the formula:
f = 1/(2π) * √(5 N/m / 5 kg)
f = 1/(2π) * √(1)
f = 0.159 Hz
Therefore, the natural frequency of the system is 0.159 Hz.
b) If mass B is displaced by 0.1 m from its equilibrium position and released, calculate the maximum displacement of mass B.
The maximum displacement of mass B can be calculated using the formula:
x = A * cos(2πft)
where x is the displacement of mass B, A is the amplitude of the motion, f is the natural frequency, and t is time.
The amplitude of the motion can be calculated as:
A = x0
where x0 is the initial displacement of mass B.
A = 0.1 m
Substituting the values in the formula:
x = 0.1 cos(2π * 0.159 t)
The maximum displacement occurs when cos(2πft) = 1, which happens at t = 0.
Therefore, the maximum displacement of mass B is:
x = 0.1 cos(0)
x = 0.1 m
Therefore, the maximum displacement of mass B is 0.1 m.
a) Calculate the natural frequency of the system.
The natural frequency of the system can be calculated using the formula:
f = 1/(2π) * √(k/m)
where f is the natural frequency, k is the spring constant, and m is the equivalent mass of the system.
The equivalent mass of the system can be calculated as:
m = m1 + m2
where m1 is the mass of mass A and m2 is the mass of mass B.
m = 2 kg + 3 kg = 5 kg
Substituting the values in the formula:
f = 1/(2π) * √(5 N/m / 5 kg)
f = 1/(2π) * √(1)
f = 0.159 Hz
Therefore, the natural frequency of the system is 0.159 Hz.
b) If mass B is displaced by 0.1 m from its equilibrium position and released, calculate the maximum displacement of mass B.
The maximum displacement of mass B can be calculated using the formula:
x = A * cos(2πft)
where x is the displacement of mass B, A is the amplitude of the motion, f is the natural frequency, and t is time.
The amplitude of the motion can be calculated as:
A = x0
where x0 is the initial displacement of mass B.
A = 0.1 m
Substituting the values in the formula:
x = 0.1 cos(2π * 0.159 t)
The maximum displacement occurs when cos(2πft) = 1, which happens at t = 0.
Therefore, the maximum displacement of mass B is:
x = 0.1 cos(0)
x = 0.1 m
Therefore, the maximum displacement of mass B is 0.1 m.
Community Answer
Two masses A & B each of 5 kg are suspended by a light inextensible st...
As A is on table so there must be book change in height if u move B. more accurate answer can be given if diagram was available
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Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.?
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Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.?.
Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.?.
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Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.?, a detailed solution for Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? has been provided alongside types of Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing motion.? theory, EduRev gives you an
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