Topic 3: Time Period & Frequency of SHM

Time Period of Simple Harmonic Motion

The time period (T) of a simple harmonic motion is the time taken by a particle to complete one full oscillation.

Frequency of SHM

The frequency (f) of SHM is the number of oscillations completed per second.

Relation Between Time Period and Frequency

f = 1 / T

T = 1 / f

Time Period of Mass–Spring System

For a mass m attached to a spring of force constant k:

T = 2π √(m / k)

Time Period of Simple Pendulum

For small oscillations of a simple pendulum of length L:

T = 2π √(L / g)

Key Points

Time period does not depend on amplitude
Frequency depends on time period
Unit of time period is second (s)
Unit of frequency is hertz (Hz)

Q1. Time period of SHM is the time taken for:
A) Half oscillation
B) One full oscillation
C) One vibration only
D) Mean to extreme

Answer: B


Q2. SI unit of time period is:
A) Hertz
B) Second
C) Minute
D) Radian

Answer: B


Q3. SI unit of frequency is:
A) Second
B) Radian
C) Hertz
D) Meter

Answer: C


Q4. Relation between frequency and time period is:
A) f = T
B) f = T²
C) f = 1 / T
D) f = 2πT

Answer: C


Q5. Time period of a mass–spring system depends on:
A) Amplitude
B) Mass and spring constant
C) Velocity
D) Displacement only

Answer: B


Q6. Formula for time period of simple pendulum is:
A) T = 2π √(g / L)
B) T = 2π √(L / g)
C) T = π √(L / g)
D) T = √(L / g)

Answer: B


Q7. If time period of a pendulum increases, its frequency:
A) Increases
B) Decreases
C) Remains same
D) Becomes zero

Answer: B


Q8. Time period of SHM is independent of:
A) Mass
B) Length
C) Amplitude
D) Force constant

Answer: C

Chapter 10: Oscillations

Topic 3: Time Period & Frequency – Quick Revision

1. Time Period (T)

Time taken to complete one full oscillation.

2. Frequency (f)

Number of oscillations per second.

3. Relation

f = 1 / T

4. Important Formulas

Mass–spring system: T = 2π √(m / k)
Simple pendulum: T = 2π √(L / g)

5. Units

Time period → second (s)
Frequency → hertz (Hz)

Exam Focus (MHT-CET)

Numericals are frequently asked using formulas for pendulum and spring–mass system.

← Topic 2: Simple Harmonic Motion Topic 4: Simple Pendulum →