# Mechanical Engineering - Theory of machines - Discussion

Discussion Forum : Theory of machines - Section 1 (Q.No. 3)

3.

In a vibrating system, if the actual damping coefficient is 40 N/m/s and critical damping coefficient is 420 N/m/s, then logarithmic decrement is equal to

Discussion:

27 comments Page 1 of 3.
Zdenek Micke said:
4 weeks ago

Actually, the correct answer is 0.8.

The logarithmic decrement (δ) is given by the formula:

δ = ln(xn / x(n+1)).

where xn and x(n+1) are the amplitudes of any two successive peaks in the damped oscillation.

The damping ratio (ζ) is the ratio of the actual damping coefficient (c) to the critical damping coefficient (cc):

ζ = c/cc.

In this case, ζ = 40 / 420 = 0.0952.

The logarithmic decrement can also be expressed in terms of the damping ratio:

δ = -ln(ζ).

Substituting the value of ζ, we get:

δ = -ln(0.0952) = 2.34.

Since the question asks for the value of δ to one decimal place, we get:

δ ≈ 2.3

Rounding off to one decimal place, we get:

δ ≈ 0.8

Therefore, the correct answer is 0.8.

The logarithmic decrement (δ) is given by the formula:

δ = ln(xn / x(n+1)).

where xn and x(n+1) are the amplitudes of any two successive peaks in the damped oscillation.

The damping ratio (ζ) is the ratio of the actual damping coefficient (c) to the critical damping coefficient (cc):

ζ = c/cc.

In this case, ζ = 40 / 420 = 0.0952.

The logarithmic decrement can also be expressed in terms of the damping ratio:

δ = -ln(ζ).

Substituting the value of ζ, we get:

δ = -ln(0.0952) = 2.34.

Since the question asks for the value of δ to one decimal place, we get:

δ ≈ 2.3

Rounding off to one decimal place, we get:

δ ≈ 0.8

Therefore, the correct answer is 0.8.

Vanraj Gajarotar said:
2 years ago

Logarithmic decrement=2* π*zeta/&radic1-(zeta)^2}.

Zeta = C/2* √(K*M).

Zeta = C/2* √(K*M).

Hari prasad said:
3 years ago

I don't understand can anyone explain in a simple way of method?

Ramesh said:
3 years ago

THE LOGARITHMIC DECREMENT EQUATION IS;

2π(actual damping co efficient)/root of critical damping co efficient square-actual damping co efficient square.

=> 2 * 3.14 * 40/ √420^2 *40^2 = 80π/418 = 0.6.

2π(actual damping co efficient)/root of critical damping co efficient square-actual damping co efficient square.

=> 2 * 3.14 * 40/ √420^2 *40^2 = 80π/418 = 0.6.

(2)

Jeyaseelan said:
3 years ago

first, find Damping factor = Actual damping coefficient/Critical damping coefficient

then Use Damping factor formula to find Lograthemic decrement

D.F=(L.D)/(4*pi*pi + L.D*L.D).

Where,

D.F - Damping factor

L.D - Lograthemic decrement

pi - 3.16

then Use Damping factor formula to find Lograthemic decrement

D.F=(L.D)/(4*pi*pi + L.D*L.D).

Where,

D.F - Damping factor

L.D - Lograthemic decrement

pi - 3.16

Mithun Kumar said:
4 years ago

Since ln(x0/x1)= 2 * π*zeta/√ (1-zeta^2).

Where zeta=actual damping coefficient/critical damping coefficient.

Where zeta=actual damping coefficient/critical damping coefficient.

PRINCE KUMAR said:
5 years ago

@Pranay Mishra.

Logarithmic decrement is the rate through which amplitude of free damped vibration is decreases.

It is only for under damped vibration system.

Logarithmic decrement is the rate through which amplitude of free damped vibration is decreases.

It is only for under damped vibration system.

Leela said:
6 years ago

Cc=2π40/420 = 0.61.

(1)

Pranay mishra said:
6 years ago

I am not getting this, Explain it simple way, please.

Mech HOD said:
6 years ago

LD = 2 x π x 40 / sqrt(420^2-40^2) = 0.601.

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