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The equation of motion for a vibrating system with viscous damping is
d2x / dt2 + c/m X dx / dt + s/m X x = 0
If the roots of this equation are real, then the system will be
- a)over-damped
- b)under-damped
- c)critically damped
- d)none of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The equation of motion for a vibrating system with viscous damping is...
- When the roots are real, overdamping takes place.
- When the roots are complex conjugate under-damping takes place.
Most Upvoted Answer
The equation of motion for a vibrating system with viscous damping is...
Explanation:
The equation of motion for a vibrating system with viscous damping is given as:
d^2x/dt^2 + (c/m) dx/dt + (s/m) x = 0
where,
x = displacement of the system from its equilibrium position
t = time
m = mass of the system
c = damping coefficient
s = stiffness coefficient
The roots of this equation can be obtained using the characteristic equation:
m^2 + (c/m) m + (s/m) = 0
The roots of this equation are given by:
m1,2 = (-c/2m) ± sqrt[(c/2m)^2 - (s/m)]
If the roots are real, then the system will be over-damped, under-damped or critically damped.
If (c/2m)^2 > (s/m), then the roots are real and distinct, and the system is over-damped.
If (c/2m)^2 < (s/m),="" then="" the="" roots="" are="" complex="" conjugates,="" and="" the="" system="" is="" />
If (c/2m)^2 = (s/m), then the roots are real and equal, and the system is critically damped.
Therefore, if the roots of the equation of motion for a vibrating system with viscous damping are real, then the system will be over-damped.
The equation of motion for a vibrating system with viscous damping is given as:
d^2x/dt^2 + (c/m) dx/dt + (s/m) x = 0
where,
x = displacement of the system from its equilibrium position
t = time
m = mass of the system
c = damping coefficient
s = stiffness coefficient
The roots of this equation can be obtained using the characteristic equation:
m^2 + (c/m) m + (s/m) = 0
The roots of this equation are given by:
m1,2 = (-c/2m) ± sqrt[(c/2m)^2 - (s/m)]
If the roots are real, then the system will be over-damped, under-damped or critically damped.
If (c/2m)^2 > (s/m), then the roots are real and distinct, and the system is over-damped.
If (c/2m)^2 < (s/m),="" then="" the="" roots="" are="" complex="" conjugates,="" and="" the="" system="" is="" />
If (c/2m)^2 = (s/m), then the roots are real and equal, and the system is critically damped.
Therefore, if the roots of the equation of motion for a vibrating system with viscous damping are real, then the system will be over-damped.
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The equation of motion for a vibrating system with viscous damping isd2x / dt2 + c/m X dx / dt + s/m X x = 0If the roots of this equation are real, then the system will bea)over-dampedb)under-dampedc)critically dampedd)none of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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