GATE Exam > GATE Questions > A single degree of freedom spring mass system...
Start Learning for Free
A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm
Correct answer is '20'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A single degree of freedom spring mass system with viscous damping has...
Most Upvoted Answer
A single degree of freedom spring mass system with viscous damping has...
Hypothesis:
We are given a single degree of freedom spring mass system with viscous damping. The system has a spring constant of 10kN/m and is excited by a sinusoidal force of amplitude 100 N. The damping factor (ratio) is 0.25. We need to find the amplitude of steady-state oscillation at resonance.
Formula:
The equation of motion for a single degree of freedom spring mass system with viscous damping can be written as:
m*x'' + c*x' + k*x = F(t)
Where,
m = mass of the system (kg)
x = displacement of the mass from equilibrium position (m)
c = damping coefficient (N.s/m)
k = spring constant (N/m)
F(t) = external force (N)
Analysis:
Step 1: Calculation of Damping Coefficient (c)
Given damping factor (ratio) = 0.25
To calculate damping coefficient (c), we can use the formula:
c = 2 * damping factor * sqrt(m * k)
Given m = 1 kg and k = 10 kN/m, we can substitute these values to find c.
c = 2 * 0.25 * sqrt(1 * 10 * 1000) = 2 * 0.25 * sqrt(10000) = 2 * 0.25 * 100 = 50 N.s/m
Step 2: Calculation of Resonant Frequency (ωn)
The resonant frequency (ωn) can be calculated using the formula:
ωn = sqrt(k / m)
Given k = 10 kN/m and m = 1 kg, we can substitute these values to find ωn.
ωn = sqrt(10000 / 1) = sqrt(10000) = 100 rad/s
Step 3: Calculation of Amplitude of Steady State Oscillation (Xss)
At resonance, the amplitude of steady-state oscillation (Xss) can be calculated using the formula:
Xss = (F(t) / k) / sqrt((1 - ω / ωn)^2 + (2 * damping factor * ω / ωn)^2)
Given F(t) = 100 N and ω = ωn (as we are considering resonance), we can substitute these values to find Xss.
Xss = (100 / 10000) / sqrt((1 - 1)^2 + (2 * 0.25 * 1)^2) = 0.01 / sqrt(0 + 0.25) = 0.01 / sqrt(0.25) = 0.01 / 0.5 = 0.02 m = 20 mm
Therefore, the amplitude of steady-state oscillation at resonance is 20 mm.
We are given a single degree of freedom spring mass system with viscous damping. The system has a spring constant of 10kN/m and is excited by a sinusoidal force of amplitude 100 N. The damping factor (ratio) is 0.25. We need to find the amplitude of steady-state oscillation at resonance.
Formula:
The equation of motion for a single degree of freedom spring mass system with viscous damping can be written as:
m*x'' + c*x' + k*x = F(t)
Where,
m = mass of the system (kg)
x = displacement of the mass from equilibrium position (m)
c = damping coefficient (N.s/m)
k = spring constant (N/m)
F(t) = external force (N)
Analysis:
Step 1: Calculation of Damping Coefficient (c)
Given damping factor (ratio) = 0.25
To calculate damping coefficient (c), we can use the formula:
c = 2 * damping factor * sqrt(m * k)
Given m = 1 kg and k = 10 kN/m, we can substitute these values to find c.
c = 2 * 0.25 * sqrt(1 * 10 * 1000) = 2 * 0.25 * sqrt(10000) = 2 * 0.25 * 100 = 50 N.s/m
Step 2: Calculation of Resonant Frequency (ωn)
The resonant frequency (ωn) can be calculated using the formula:
ωn = sqrt(k / m)
Given k = 10 kN/m and m = 1 kg, we can substitute these values to find ωn.
ωn = sqrt(10000 / 1) = sqrt(10000) = 100 rad/s
Step 3: Calculation of Amplitude of Steady State Oscillation (Xss)
At resonance, the amplitude of steady-state oscillation (Xss) can be calculated using the formula:
Xss = (F(t) / k) / sqrt((1 - ω / ωn)^2 + (2 * damping factor * ω / ωn)^2)
Given F(t) = 100 N and ω = ωn (as we are considering resonance), we can substitute these values to find Xss.
Xss = (100 / 10000) / sqrt((1 - 1)^2 + (2 * 0.25 * 1)^2) = 0.01 / sqrt(0 + 0.25) = 0.01 / sqrt(0.25) = 0.01 / 0.5 = 0.02 m = 20 mm
Therefore, the amplitude of steady-state oscillation at resonance is 20 mm.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer?
Question Description
A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer?.
A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer?.
Solutions for A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer?, a detailed solution for A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? has been provided alongside types of A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor(ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mmCorrect answer is '20'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup