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GRADE 9 PRACTICE

Physics Problems: Mechanical oscillations, Grade 9

Pendulums, harmonic, free and forced vibrations.

18 problems across 3 sub-topics
Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

The answer options are there to check against, and the walkthrough opens under each problem.

18 problems
Position in this set: 1 from 18

Problem #28

Oscillation parameters and pendulums

What concept does the description correspond to: “The system is capable of repeatedly moving around a stable equilibrium position due to the restoring effect and inertia.”?

Answer options

  1. \text{Oscillatory system}
  2. \text{Amplitude, period and frequency}
  3. \text{Simple pendulums and mass–spring oscillators}
  4. \text{Point particle}
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Given
\text{Description}
\text{A system can move repeatedly about stable equilibrium through restoring action and inertia.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    In both a pendulum and a mass–spring system, energy shifts between kinetic and potential forms.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Oscillatory system}

Answer\text{Concept} = \text{Oscillatory system}

Position in this set: 2 from 18

Problem #29

Oscillation parameters and pendulums

What concept does the description correspond to: “Amplitude specifies the maximum deviation, period specifies the cycle time, and frequency specifies the number of cycles per second.”?

Answer options

  1. \text{Amplitude, period and frequency}
  2. \text{Oscillatory system}
  3. \text{Simple pendulums and mass–spring oscillators}
  4. \text{Point particle}
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Given
\text{Description}
\text{Amplitude gives the maximum displacement; period gives cycle time; frequency gives cycles per second.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    Period and frequency are reciprocals; measurements over several cycles reduce relative error.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Amplitude, period and frequency}

Answer\text{Concept} = \text{Amplitude, period and frequency}

Position in this set: 3 from 18

Problem #30

Oscillations

The pendulum completed 20 complete oscillations in 10 s. Find the period and frequency.

Answer options

  1. 0{,}5\,\text{с};\ 2\,\text{Гц}
  2. 2\,\text{с};\ 0{,}5\,\text{Гц}
  3. 0{,}5\,\text{с};\ 20\,\text{Гц}
  4. 10\,\text{с};\ 2\,\text{Гц}
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Given
N
20
t
10\,\text{с}
Find

T\nu

  1. T=\frac{t}{N}T=\frac{10}{20}\,\text{с}T = 0{,}5\,\text{с}
  2. \nu=\frac{N}{t}\nu=\frac{20}{10}\,\text{Гц}\nu = 2\,\text{Гц}

Answer0{,}5\,\text{с}2\,\text{Гц}

Position in this set: 4 from 18

Problem #31

Harmonic, damped and forced oscillations

What concept does the description correspond to: “Damped oscillations lose amplitude due to resistance, while forced oscillations are supported by an external periodic force.”?

Answer options

  1. \text{Damped and forced oscillations}
  2. \text{Harmonic oscillations}
  3. \text{Resonance}
  4. \text{Point particle}
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Given
\text{Description}
\text{Damped oscillations decrease in amplitude because of resistance; forced oscillations are maintained by an external periodic force.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    After the transient dies away, the driven system oscillates at the driving frequency.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Damped and forced oscillations}

Answer\text{Concept} = \text{Damped and forced oscillations}

Position in this set: 5 from 18

Problem #32

Harmonic, damped and forced oscillations

What concept does the description correspond to: “Oscillations in which the coordinate changes according to the law of sine or cosine with a constant frequency.”?

Answer options

  1. \text{Harmonic oscillations}
  2. \text{Damped and forced oscillations}
  3. \text{Resonance}
  4. \text{Point particle}
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Given
\text{Description}
\text{Oscillations whose coordinate follows a sine or cosine law at constant frequency.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    Phase specifies the oscillator's state at a chosen instant and allows different oscillations to be compared.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Harmonic oscillations}

Answer\text{Concept} = \text{Harmonic oscillations}

Position in this set: 6 from 18

Problem #33

Oscillations

The natural frequency of a weakly damped system is 5 Hz. At what frequency of a weak periodic force is the largest steady-state amplitude expected?

Answer options

  1. 5\,\text{Гц}
  2. 0\,\text{Гц}
  3. 2{,}5\,\text{Гц}
  4. 10\,\text{Гц}
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Given
\nu_0
5\,\text{Гц}
Find

\nu

  1. \nu\approx\nu_0

    Resonance occurs when the frequency of influence is close to the natural frequency.

  2. \nu=5\,\text{Гц}

Answer5\,\text{Гц}

Position in this set: 7 from 18

Problem #118

Oscillation parameters and pendulums

For 30 with the pendulum committed 20 complete hesitation. Find the period.

Answer options

  1. 1{,}5\,\text{с}
  2. 3\,\text{с}
  3. 0{,}75\,\text{с}
  4. 4{,}5\,\text{с}
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Given
t
30\,\text{с}
N
20\,\text{колебаний}
Find

T

  1. T=\frac{t}{N}T=\frac{30}{20}T=1{,}5\,\text{с}

    A period is the time of one complete oscillation.

Answer1{,}5\,\text{с}

Position in this set: 8 from 18

Problem #119

Oscillation parameters and pendulums

For 40 with the pendulum committed 25 complete hesitation. Find the period.

Answer options

  1. 3{,}2\,\text{с}
  2. 1{,}6\,\text{с}
  3. 0{,}8\,\text{с}
  4. 4{,}8\,\text{с}
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Given
t
40\,\text{с}
N
25\,\text{колебаний}
Find

T

  1. T=\frac{t}{N}T=\frac{40}{25}T=1{,}6\,\text{с}

    A period is the time of one complete oscillation.

Answer1{,}6\,\text{с}

Position in this set: 9 from 18

Problem #120

Oscillation parameters and pendulums

Oscillation period 0{,}5 s. How many complete oscillations will occur in 2 min?

Answer options

  1. 480\,\text{колебаний}
  2. 240\,\text{колебаний}
  3. 120\,\text{колебаний}
  4. 720\,\text{колебаний}
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Given
T
0{,}5\,\text{с}
t
2\,\text{мин}
Find

N

  1. a=60ta=2 \cdot 60a=120\,\text{с}

    We reduce time to seconds.

  2. N=\frac{a}{T}N=\frac{120}{0{,}5}N=240\,\text{колебаний}

    We divide the total time into a period.

Answer240\,\text{колебаний}

Position in this set: 10 from 18

Problem #121

Oscillation parameters and pendulums

Oscillation period 0{,}8 s. How many complete oscillations will occur in 4 min?

Answer options

  1. 600\,\text{колебаний}
  2. 150\,\text{колебаний}
  3. 300\,\text{колебаний}
  4. 900\,\text{колебаний}
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Given
T
0{,}8\,\text{с}
t
4\,\text{мин}
Find

N

  1. a=60ta=4 \cdot 60a=240\,\text{с}

    We reduce time to seconds.

  2. N=\frac{a}{T}N=\frac{240}{0{,}8}N=300\,\text{колебаний}

    We divide the total time into a period.

Answer300\,\text{колебаний}

Position in this set: 11 from 18

Problem #122

Oscillation parameters and pendulums

Oscillation amplitude 5 cm, period 2 s. How far in meters will the point travel? 20 s? Time is equal to an integer number of periods.

Answer options

  1. 4\,\text{м}
  2. 1\,\text{м}
  3. 2\,\text{м}
  4. 6\,\text{м}
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Given
A
5\,\text{см}
T
2\,\text{с}
t
20\,\text{с}
Find

S

  1. N=\frac{t}{T}N=\frac{20}{2}N=10\,\text{колебаний}

    We determine the number of complete oscillations.

  2. a=\frac{A}{100}a=\frac{5}{100}a=0{,}05\,\text{м}

    Convert the amplitude to meters.

  3. S=4aNS=4 \cdot 0{,}05 \cdot 10S=2\,\text{м}

    During a period, a point passes through four amplitudes.

Answer2\,\text{м}

Position in this set: 12 from 18

Problem #123

Oscillation parameters and pendulums

Oscillation amplitude 8 cm, period 4 s. How far in meters will the point travel? 40 s? Time is equal to an integer number of periods.

Answer options

  1. 6{,}4\,\text{м}
  2. 1{,}6\,\text{м}
  3. 9{,}6\,\text{м}
  4. 3{,}2\,\text{м}
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Given
A
8\,\text{см}
T
4\,\text{с}
t
40\,\text{с}
Find

S

  1. N=\frac{t}{T}N=\frac{40}{4}N=10\,\text{колебаний}

    We determine the number of complete oscillations.

  2. a=\frac{A}{100}a=\frac{8}{100}a=0{,}08\,\text{м}

    Convert the amplitude to meters.

  3. S=4aNS=4 \cdot 0{,}08 \cdot 10S=3{,}2\,\text{м}

    During a period, a point passes through four amplitudes.

Answer3{,}2\,\text{м}

Position in this set: 13 from 18

Problem #124

Harmonic, damped and forced oscillations

Period of free oscillations of the system 0{,}25 s. Find your natural frequency.

Answer options

  1. 8\,\text{Гц}
  2. 4\,\text{Гц}
  3. 2\,\text{Гц}
  4. 12\,\text{Гц}
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Given
T
0{,}25\,\text{с}
Find

f

  1. f=\frac{1}{T}f=\frac{1}{0{,}25}f=4\,\text{Гц}

    Frequency and period are mutually inverse.

Answer4\,\text{Гц}

Position in this set: 14 from 18

Problem #125

Harmonic, damped and forced oscillations

Period of free oscillations of the system 0{,}2 s. Find your natural frequency.

Answer options

  1. 10\,\text{Гц}
  2. 2{,}5\,\text{Гц}
  3. 5\,\text{Гц}
  4. 15\,\text{Гц}
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Given
T
0{,}2\,\text{с}
Find

f

  1. f=\frac{1}{T}f=\frac{1}{0{,}2}f=5\,\text{Гц}

    Frequency and period are mutually inverse.

Answer5\,\text{Гц}

Position in this set: 15 from 18

Problem #126

Harmonic, damped and forced oscillations

For 12 with the system committed 30 free vibrations. What frequency of external influence should be chosen for resonance with weak attenuation?

Answer options

  1. 5\,\text{Гц}
  2. 1{,}25\,\text{Гц}
  3. 2{,}5\,\text{Гц}
  4. 7{,}5\,\text{Гц}
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Given
t
12\,\text{с}
N
30\,\text{колебаний}
Find

f

  1. T=\frac{t}{N}T=\frac{12}{30}T=0{,}4\,\text{с}

    Finding our own period.

  2. f=\frac{1}{T}f=\frac{1}{0{,}4}f=2{,}5\,\text{Гц}

    With weak damping, the resonance is close to its natural frequency.

Answer2{,}5\,\text{Гц}

Position in this set: 16 from 18

Problem #127

Harmonic, damped and forced oscillations

For 20 with the system committed 60 free vibrations. What frequency of external influence should be chosen for resonance with weak attenuation?

Answer options

  1. 6\,\text{Гц}
  2. 1{,}5\,\text{Гц}
  3. 9\,\text{Гц}
  4. 3\,\text{Гц}
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Given
t
20\,\text{с}
N
60\,\text{колебаний}
Find

f

  1. T=\frac{t}{N}T=\frac{20}{60}T=0{,}333333\,\text{с}

    Finding our own period.

  2. f=\frac{1}{T}f=\frac{1}{0{,}333333}f=3\,\text{Гц}

    With weak damping, the resonance is close to its natural frequency.

Answer3\,\text{Гц}

Position in this set: 17 from 18

Problem #128

Harmonic, damped and forced oscillations

Initial amplitude 20 cm. After each complete oscillation it is 0{,}5 from the previous one. Find the amplitude after three vibrations.

Answer options

  1. 5\,\text{см}
  2. 1{,}25\,\text{см}
  3. 7{,}5\,\text{см}
  4. 2{,}5\,\text{см}
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Given
A
20\,\text{см}
r
0{,}5\,\text{доля}
Find

A_3

  1. A_1=ArA_1=20 \cdot 0{,}5A_1=10\,\text{см}

    We apply the attenuation law specified by the condition.

  2. A_2=A_1rA_2=10 \cdot 0{,}5A_2=5\,\text{см}

    The current amplitude decreases, not the original one every time.

  3. A_3=A_2rA_3=5 \cdot 0{,}5A_3=2{,}5\,\text{см}

    We repeat the calculation for the third period.

Answer2{,}5\,\text{см}

Position in this set: 18 from 18

Problem #129

Harmonic, damped and forced oscillations

Initial amplitude 16 cm. After each complete oscillation it is 0{,}75 from the previous one. Find the amplitude after three vibrations.

Answer options

  1. 6{,}75\,\text{см}
  2. 13{,}5\,\text{см}
  3. 3{,}375\,\text{см}
  4. 20{,}25\,\text{см}
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Given
A
16\,\text{см}
r
0{,}75\,\text{доля}
Find

A_3

  1. A_1=ArA_1=16 \cdot 0{,}75A_1=12\,\text{см}

    We apply the attenuation law specified by the condition.

  2. A_2=A_1rA_2=12 \cdot 0{,}75A_2=9\,\text{см}

    The current amplitude decreases, not the original one every time.

  3. A_3=A_2rA_3=9 \cdot 0{,}75A_3=6{,}75\,\text{см}

    We repeat the calculation for the third period.

Answer6{,}75\,\text{см}

The theory behind these problems

Work through the topic if a problem will not give in.

Oscillation parameters and pendulumsAmplitude, period, frequency, phase, simple pendulums and mass–spring oscillators.Harmonic, damped and forced oscillationsHarmonic law, energy loss and resonance.

Formulas by topic

Look up symbols and units of measurement in the reference.

AmplitudeA, xₘ · мPeriodT · сFrequencyν · ГцAngular frequencyω · с⁻¹