Lesson test: Free oscillation and damping

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Free oscillation and damping

1.[2p]
A 0.25 kg mass hangs on a spring of stiffness 100 N m⁻¹. What is $ω_{0}$ in radians per second?

CorrectNot quite: 20

2.[3p]
A system has $m = 4$ kg, $k = 100$ N m⁻¹ and $c = 20$ N s m⁻¹. What is the damping ratio $ζ$ ?

CorrectNot quite: 0.5

3.[3p]
An oscillator has $ω_{0} = 10$ rad s⁻¹ and $ζ = 0.6$ . What is the damped frequency $ω_{d}$ in radians per second?

CorrectNot quite: 8

4.[1p]
Increasing the damping beyond critical makes the system return to equilibrium faster.

True

The answer is: False

False

Correct

5.[2p]
What is special about critical damping?

It is the fastest return to equilibrium with no overshoot

Correct

It is the point at which all motion stops instantly

The answer is: It is the fastest return to equilibrium with no overshoot

It gives the largest possible oscillation amplitude

The answer is: It is the fastest return to equilibrium with no overshoot

It makes the damped frequency equal the natural frequency

The answer is: It is the fastest return to equilibrium with no overshoot

6.[3p]
Successive peaks on a decay trace measure 10.0 mm and 6.0 mm. What is the damping ratio $ζ$ ?

CorrectNot quite: 0.081

7.[3p]
A series circuit has $L = 2$ mH and $C = 50$ nF. What is $ω_{0}$ in radians per second?

CorrectNot quite: 100000

8.[3p]
Match each device to the damping it is designed for.

Door closer
Analogue meter movement
Car suspension
Tuning fork

overdamped
as lightly damped as possible
underdamped, around 0.3
critically damped

Show the answer

Door closer: overdamped Analogue meter movement: critically damped Car suspension: underdamped, around 0.3 Tuning fork: as lightly damped as possible

9.[3p]
Which statements about the series RLC circuit are correct?

Select all that apply

Inductance plays the part of mass and resistance the part of the dashpot

Correct

The natural frequency is $1 / \sqrt{L C}$

Correct

Critical damping needs $R = 2 \sqrt{L / C}$

Correct

Capacitance plays the part of the dashpot

The answer is: Inductance plays the part of mass and resistance the part of the dashpot, The natural frequency is $1/\sqrt{LC}$, Critical damping needs $R = 2\sqrt{L/C}$

1.[2p] A 0.25 kg mass hangs on a spring of stiffness 100 N m⁻¹. What is ω0 in radians per second?

2.[3p] A system has m=4 kg, k=100 N m⁻¹ and c=20 N s m⁻¹. What is the damping ratio ζ?

3.[3p] An oscillator has ω0=10 rad s⁻¹ and ζ=0.6. What is the damped frequency ωd in radians per second?

4.[1p] Increasing the damping beyond critical makes the system return to equilibrium faster.

5.[2p] What is special about critical damping?

6.[3p] Successive peaks on a decay trace measure 10.0 mm and 6.0 mm. What is the damping ratio ζ?

7.[3p] A series circuit has L=2 mH and C=50 nF. What is ω0 in radians per second?

8.[3p] Match each device to the damping it is designed for.

9.[3p] Which statements about the series RLC circuit are correct?

1.[2p]
A 0.25 kg mass hangs on a spring of stiffness 100 N m⁻¹. What is $ω_{0}$ in radians per second?

2.[3p]
A system has $m = 4$ kg, $k = 100$ N m⁻¹ and $c = 20$ N s m⁻¹. What is the damping ratio $ζ$ ?

3.[3p]
An oscillator has $ω_{0} = 10$ rad s⁻¹ and $ζ = 0.6$ . What is the damped frequency $ω_{d}$ in radians per second?

4.[1p]
Increasing the damping beyond critical makes the system return to equilibrium faster.

5.[2p]
What is special about critical damping?

6.[3p]
Successive peaks on a decay trace measure 10.0 mm and 6.0 mm. What is the damping ratio $ζ$ ?

7.[3p]
A series circuit has $L = 2$ mH and $C = 50$ nF. What is $ω_{0}$ in radians per second?

8.[3p]
Match each device to the damping it is designed for.

9.[3p]
Which statements about the series RLC circuit are correct?