PhysicsICSE Class 10 · Vibrations and Resonance

Forced Vibrations: Meaning, Examples and Differences (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Forced vibrations are the vibrations of a body under an external periodic force, at the frequency of that force rather than its own natural frequency. Their amplitude is usually small and they stop when the force is removed. A tabletop vibrating when a sounding fork's stem is pressed on it is the standard example.

The table is forced to vibrate at the fork's frequency, and its large surface sends out louder sound, which stops when the fork is removed.

Illustration drawn for QuestionBuddy.

Understand Forced Vibrations: Meaning and Examples

What makes a vibration 'forced'. Every body has its own natural frequency, at which it vibrates if disturbed and left alone. Now suppose an external periodic force keeps acting on it: a vibrating fork pressed against it, an engine shaking it, a sound wave pushing on it. The body is made to vibrate at the frequency of the applied force, whatever its own natural frequency. These are forced vibrations, and the external body is called the driver.

Features of forced vibrations.
1. Frequency = frequency of the applied force (the driver), not the natural frequency of the body.
2. Amplitude is usually small. It depends on how close the driver's frequency is to the body's natural frequency: the closer they are, the larger the amplitude. It also depends on the damping.
3. They last only as long as the force acts; when the driver stops, the body soon stops (or goes back to vibrating at its own frequency, dying away).
4. In the special case where the applied frequency equals the natural frequency, the amplitude becomes very large: resonance.

The tabletop experiment. Strike a tuning fork; its sound is faint, because its thin prongs set only a little air vibrating. Press its stem on a table: the sound becomes much louder. The fork forces the tabletop to vibrate at the fork's frequency (forced vibrations). The table has a large surface area, so it sets a much larger mass of air vibrating, which sends more sound energy to the ear. The sound also dies away sooner, because the energy is now given out faster. The table's vibrations are forced, not resonant: the table would vibrate in this way with a fork of any frequency.

Uses of forced vibrations.

Sound boards and sound boxes of guitars, sitars, violins and pianos: the strings force the board and the air inside to vibrate, making the sound louder.
Loudspeakers: the cone is forced by the electrical signal to vibrate at the frequency of the music.
Our eardrum is forced to vibrate at the frequency of the sound reaching it, which is how we hear every pitch.
A microphone diaphragm vibrates at the frequency of the sound falling on it.

Unwanted forced vibrations. A running engine makes the body panels and mirrors of a car vibrate at the engine's frequency; a passing heavy lorry makes window panes rattle; an unbalanced ceiling fan shakes a hanging lamp. Engineers use rubber mountings and dampers to reduce them.

Natural vs forced vibrations.

Natural (free) vibrations	Forced vibrations
No external periodic force after the start	Continuous external periodic force
Frequency is the natural frequency of the body	Frequency is that of the applied force
Amplitude constant (ideally)	Amplitude usually small; depends on how close the two frequencies are
Continue after the initial disturbance	Stop soon after the force is removed

Damped vs forced. Do not confuse the two. Damped vibrations are free vibrations whose amplitude falls because of resistance; forced vibrations are maintained by a driver and can have a steady amplitude, larger or smaller depending on the frequency match.

Forced Vibrations: Meaning and Examples: formulas and key facts

Frequency of forced vibrations: $f_{forced} = f_{applied}$; The body follows the driver, not its own natural frequency.
Frequency and period: $f = \frac{1}{T}$; Revolutions or strokes per minute ÷ 60 gives Hz.
Wavelength of the sound produced: $v = f λ$; The sound has the driver's frequency.
Forced vibrations at a glance: Frequency same as the applied force
Amplitude small unless the frequencies match
Duration only while the force acts
Special case resonance when the frequencies are equal; Four facts examiners test.

Frequency	same as the applied force
Amplitude	small unless the frequencies match
Duration	only while the force acts
Special case	resonance when the frequencies are equal

How to solve Forced Vibrations: Meaning and Examples questions

Classify the vibration first, then state its frequency and amplitude.

1Is there an external periodic force? No: natural (or damped) vibration. Yes: forced vibration.
2Compare the driver's frequency with the body's natural frequency: equal means resonance; different means ordinary forced vibration with small amplitude.
3State the frequency of the body's vibration: the driver's frequency.
4For 'why louder', mention the large vibrating surface setting more air into vibration.
5For numbers, convert rpm or strokes per minute to Hz ( $\div 60$ ), then use $T = \frac{1}{f}$ and $λ = \frac{v}{f}$ .

Forced Vibrations: Meaning and Examples in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

A rattling car mirror

Suppose a car's engine idles at 1800 revolutions per minute and the side mirror shakes, blurring the image.

At what frequency does the mirror vibrate, and what kind of vibration is this?

Try it first, then show the solutionSolution

Engine frequency $= \frac{1800}{60} = 30$ Hz.
The engine applies a periodic force through the car body; the mirror vibrates at 30 Hz whatever its natural frequency: forced vibrations.

Answer: 30 Hz; forced vibrations.

Memory hook: The driver sets the beat; the body dances to it.

Why a guitar needs a hollow body

Imagine plucking a guitar string stretched on a solid wooden plank, and then the same string on a real guitar with a hollow body.

Why is the guitar much louder?

Try it first, then show the solutionSolution

The vibrating string forces the guitar's sound board and the air inside the hollow body to vibrate at the string's frequency.
This large vibrating surface and air mass push on much more of the surrounding air, so more sound energy reaches the listener.

Answer: Forced vibrations of the large sound board and enclosed air make the sound louder.

Memory hook: Big surface, big sound.

Tricks to remember Forced Vibrations: Meaning and Examples

Short memory aids. Say each one aloud once, then use it on a question the same day.

Follow the leader
In forced vibrations the body is a follower: it takes the leader's (driver's) frequency.
Use it when: Stating the frequency of forced vibrations.
FAD: Frequency, Amplitude, Duration
Frequency of the driver; Amplitude small; Duration only while forced.
Use it when: Listing features.
Table makes it loud, not resonant
A table sounds with any fork: forced. Only one special length or setting sounds loudest: resonance.
Use it when: The tabletop multiple-choice question.
Damped falls, forced follows
Damped amplitude falls; forced frequency follows the driver.
Use it when: Keeping damped and forced apart.

Forced Vibrations: Meaning and Examples: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Frequency of forced vibrations · 1 mark · MCQBoard level

A body executing forced vibrations vibrates with:
(a) its own natural frequency
(b) the frequency of the applied periodic force
(c) a frequency that keeps decreasing
(d) zero frequency

Try it first, then show the solutionSolution

In forced vibrations the body follows the driver's frequency.

Answer: (b) the frequency of the applied periodic force

Example 2: Defining forced vibrations · 3 marks · Short answerBoard level

(a) What are forced vibrations? (b) Give two examples. (c) How does their amplitude compare with that at resonance?

Try it first, then show the solutionSolution

(a) Vibrations of a body under an external periodic force, at the frequency of the applied force. (1)
(b) Any two: a tabletop vibrating with a fork's stem pressed on it; a guitar's sound board; a loudspeaker cone; the eardrum. (1)
(c) Usually small; at resonance the amplitude is very large. (1)

Answer: (a) Vibrations at the frequency of an applied periodic force (b) Tabletop, sound board (any two) (c) Small, compared with very large at resonance

Example 3: Engine and mirror · 3 marks · Short answerHarder board level

A motorbike engine runs at 2400 rpm. (a) Find the frequency of the periodic force it applies to the handlebar mirror. (b) Find the time period of the mirror's vibration. (c) What would happen to the mirror's frequency if the engine speed were doubled?

Try it first, then show the solutionSolution

(a) $f = \frac{2400}{60} = 40$ Hz. (1)
(b) $T = \frac{1}{40} = 0.025$ s. (1)
(c) It would double to 80 Hz: a forced vibration always has the driver's frequency. (1)

Answer: (a) 40 Hz (b) 0.025 s (c) It doubles to 80 Hz

Example 4: Fork on a tabletop · 4 marks · Short answerHarder board level

A 480 Hz tuning fork is struck and its stem is pressed on a wooden table. (a) Why does the sound become louder? (b) At what frequency does the tabletop vibrate? (c) Find the wavelength of the sound in air (speed 336 m/s). (d) Why does the sound now last a shorter time?

Try it first, then show the solutionSolution

(a) The fork forces the tabletop to vibrate; its large surface sets a large mass of air vibrating, sending more sound energy to the ear. (1)
(b) 480 Hz, the frequency of the fork (forced vibrations). (1)
(c) $λ = \frac{336}{480} = 0.7$ m. (1)
(d) The fork's energy is given out to the air much faster through the large table, so it is used up sooner. (1)

Answer: (a) Forced vibration of a large surface (b) 480 Hz (c) 0.7 m (d) Energy is radiated faster

Example 5: Natural or forced? · 2 marks · Short answerHarder board level

Classify each as natural, damped, forced vibration or resonance: (a) a guitar's sound board while the string is played; (b) a swing left to slow down by itself; (c) an air column that suddenly sounds loudly as a fork is held over it; (d) a struck tuning fork held in the air.

Try it first, then show the solutionSolution

(a) Forced; (b) damped. (1)
(c) Resonance; (d) natural (free) vibration, slowly damped by the air. (1)

Answer: (a) Forced (b) Damped (c) Resonance (d) Natural

Example 6: A loudspeaker cone · 3 marks · Short answerHOTS / competency

A loudspeaker plays a steady 1 kHz test tone. (a) Find the time period of its cone's vibration. (b) How many vibrations does the cone make in 0.5 s? (c) Explain why the cone's vibrations are forced, not natural.

Try it first, then show the solutionSolution

(a) $T = \frac{1}{1000} = 1 0^{- 3}$ s $= 1$ ms. (1)
(b) $N = f t = 1000 \times 0.5 = 500$ . (1)
(c) The cone is driven by a periodic electrical force and vibrates at the signal's frequency, which changes as the music changes; it stops when the signal stops. (1)

Answer: (a) 1 ms (b) 500 (c) It follows the frequency of the applied signal

Example 7: Case study: a classroom demonstration · 4 marks · Case-basedHOTS / competency

A teacher sounds a tuning fork and holds it in the air; the class hears a faint note for about 20 s. She strikes it again and presses its stem on the hollow wooden box of a sonometer; the note is much louder but dies in about 5 s.
(a) Name the type of vibration of the fork when held in the air.
(b) Name the type of vibration of the wooden box. At what frequency does it vibrate?
(c) Explain why the sound is louder on the box.
(d) Explain why it dies away sooner.

Try it first, then show the solutionSolution

(a) Natural vibrations, slowly damped by the air. (1)
(b) Forced vibrations, at the frequency of the fork. (1)
(c) The box and the air inside it present a large vibrating surface, setting much more air into vibration. (1)
(d) With the same energy given out much faster, the fork's energy is used up in a shorter time. (1)

Answer: (a) Natural (damped) (b) Forced, at the fork's frequency (c) Large vibrating surface (d) Energy radiated faster

Where students lose marks in Forced Vibrations: Meaning and Examples

The slips examiners see most often, and what to write instead.

Mistake: Calling the tabletop's vibration resonance or damped
The table vibrates under a periodic force at the fork's frequency, whatever its own frequency: that is forced vibration.
Wrong working
'The tabletop vibrations are an example of resonance.'
Right working
'They are forced vibrations.'
Do this: Resonance needs equal frequencies and a very large amplitude; a table does not need any special fork.
Usually costs: Reported by CISCE examiners for 2024 Q1(vi), where candidates chose resonance or damped vibrations.
Mistake: Giving the natural frequency as the frequency of forced vibrations
A forced body follows the driver.
Wrong working
'The mirror vibrates at its own natural frequency.'
Right working
'The mirror vibrates at 40 Hz, the engine's frequency.'
Do this: Remember: follow the leader.
Usually costs: The 1-mark answer.
Mistake: Confusing damped with forced vibrations
Damped vibrations lose amplitude because of resistance; forced vibrations are kept going by a driver and can grow or shrink with the frequency match.
Wrong working
'Forced vibrations are vibrations whose amplitude decreases.'
Right working
'Forced vibrations occur at the frequency of the applied force; damped vibrations are free vibrations with decreasing amplitude.'
Do this: Learn one defining phrase for each.
Usually costs: Examiners suggested teaching this distinction after 2024 Q1(vi).
Mistake: Explaining 'louder' without the large surface
Loudness increases because more air is set into vibration by the large surface.
Wrong working
'The table increases the frequency, so the sound is louder.'
Right working
'The table's large area sets more air vibrating at the same frequency, so the sound is louder.'
Do this: Loudness is about amplitude and the mass of air vibrating, not frequency.
Usually costs: The reason mark.

Exam tips

In MCQs, 'definitely an example of' a tabletop vibrating with a fork means forced vibrations.
State the frequency of forced vibrations in one phrase: 'equal to the frequency of the applied force'.
When explaining a sound box, use the words 'forced to vibrate', 'large surface area' and 'more air'.
Learn three differences between natural and forced vibrations as a table.

Practice questions on Forced Vibrations: Meaning and Examples

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
When the stem of a vibrating fork is pressed on a bench, the bench vibrates. These vibrations are:
(a) natural
(b) damped
(c) forced
(d) free
Hint
Is there an external periodic force?
Answer
(c) forced
Q2 · 1 mark · Very short answerBoard level
State what happens to forced vibrations when the applied force is removed.
Hint
Do they continue?
Answer
They stop soon after (the body may briefly vibrate at its own natural frequency, dying away).
Q3 · 2 marks · Short answerHarder board level
A sound of frequency 2.5 kHz reaches your ear. At what frequency does your eardrum vibrate, and what is the period of this vibration?
Hint
The eardrum is driven by the sound.
Answer
2.5 kHz (forced vibration); $T = \frac{1}{2500} = 4 \times 1 0^{- 4}$ s $= 0.4$ ms.
Q4 · 3 marks · Short answerBoard level
Give three differences between natural and forced vibrations.
Hint
Force, frequency, amplitude or duration.
Answer
(1) Natural: no external periodic force after the start; forced: a continuous periodic force acts. (2) Natural: frequency is the body's natural frequency; forced: frequency of the applied force. (3) Natural: amplitude constant in the ideal case and vibration continues; forced: amplitude usually small and vibration stops soon after the force is removed.
Q5 · 2 marks · Short answerHarder board level
The needle of a sewing machine makes 900 strokes per minute, and the light table on which the machine stands shakes. Find the frequency of the table's vibration, and name the type of vibration.
Hint
Strokes per minute ÷ 60.
Answer
$\frac{900}{60} = 15$ Hz; forced vibrations (at the machine's frequency).
Q6 · 2 marks · Short answerHarder board level
Why do stringed instruments such as the sitar have a hollow body or a gourd attached?
Hint
Size of the vibrating surface.
Answer
The strings alone set very little air vibrating. They force the hollow body and the air inside to vibrate at the same frequency; this large surface sets much more air vibrating, so the sound is louder.
Q7 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A tabletop vibrates at the frequency of a tuning fork whose stem is pressed on it, whatever the table's natural frequency.
Reason (R): In forced vibrations the body vibrates with the frequency of the applied periodic force.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
Driver's frequency.
Answer
(c) Both are true, and (R) explains (A).
Q8 · 3 marks · Short answerHOTS / competency
A tabletop has a natural frequency of about 60 Hz. Forks of 64 Hz and 256 Hz are struck equally hard and their stems pressed on it in turn. (a) At what frequency does the table vibrate in each case? (b) In which case would you expect the larger amplitude of the table's vibration? Explain. (c) Would either case be called resonance?
Hint
Amplitude grows as the frequencies get closer.
Answer
(a) 64 Hz and 256 Hz, the forks' frequencies. (b) With the 64 Hz fork: its frequency is much closer to the table's natural frequency (difference 4 Hz against 196 Hz), and the amplitude of forced vibrations is larger the closer the two frequencies are. (c) No: resonance needs the frequencies to be equal; both are forced vibrations, though the 64 Hz case is near resonance.
Q9 · 3 marks · Short answerHarder board level
A slightly unbalanced ceiling fan turns at 360 rpm, and a lampshade hanging nearby is seen to sway. (a) Find the frequency of the force on the lampshade. (b) If the fan is switched off, what happens to the lampshade's motion? (c) Suggest one way to stop the lampshade from shaking.
Hint
rpm ÷ 60.
Answer
(a) $\frac{360}{60} = 6$ Hz. (b) The forced vibration stops; the lampshade may swing briefly at its own natural frequency and then come to rest (damped). (c) Balance the fan blades, or fix the lampshade firmly or with a damping mount.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Frequency of forced vibrations?Show answer
That of the applied force.
2.Typical amplitude of forced vibrations?Show answer
Small (unless at resonance).
3.A fork's stem pressed on a table gives what type of vibration of the table?Show answer
Forced.
4.Why does a sound box make a note louder?Show answer
Its large surface sets more air vibrating.
5.When do forced vibrations become resonance?Show answer
When the applied frequency equals the natural frequency.

Forced Vibrations: Meaning and Examples: frequently asked questions

What are forced vibrations?

They are vibrations of a body under an external periodic force. The body vibrates at the frequency of that force, usually with a small amplitude, and stops soon after the force is removed.

Why does a tuning fork sound louder when its stem is pressed on a table?

The fork forces the tabletop to vibrate at its frequency. The table's large surface sets much more air vibrating than the thin prongs, so more sound energy reaches the ear.

What is the difference between forced vibrations and resonance?

In forced vibrations the applied frequency differs from the body's natural frequency and the amplitude is small. In resonance the two frequencies are equal and the amplitude becomes very large.