Physics

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Interactive Science Lab

Mass-Spring System & SHM Waveforms

Study horizontal mass-spring periodic oscillations, amplitude, period, restoring acceleration vectors, and live x-t waveform.

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Mass-Spring System & SHM Waveforms

Visualize horizontal mass-spring periodic oscillations, amplitude, time period, frequency, restoring acceleration vectors, and live x-t sine waveforms.

Class 10 Physics

Unit 10: Section 10.1

Simple Pendulum

Harmonic Oscillator Track(x = A cos(ωt))

Elapsed Time (t):0 s

Displacement (x):+5 cm

Direction:Extreme Peak

Cycles: 0

Displacement vs Time Waveform: x(t) = A cos(ωt)2 Full Periods (8s)

0s0s

Speed:

Oscillation Parameters

Quick Preset Oscillators

Amplitude (A)

1 cm5 cm10 cm

Time Period (T)

0.5 s (Fast)5 s10 s (Slow)

Oscillation Parameters

Quick Preset Oscillators

Amplitude (A)

1 cm5 cm10 cm

Time Period (T)

0.5 s (Fast)5 s10 s (Slow)

Derived Oscillation Properties

Class 9 Physics

Max displacement

seconds (s)

Time for 1 cycle

0.25

Hertz (Hz)

f = 1 / T

1.571

rad/s

ω = 2π / T

v_max

7.85

cm/s (at x=0)

v_max = A · ω

a_max

12.34

cm/s² (at x=±A)

a_max = ω² · A

Key Exam Concept: Mean vs Extreme Position Comparison

Physical Quantity	Mean Position (x = 0)	Extreme Positions (x = ±A)
Displacement (x)	0 cm (Zero)	±5 cm (Maximum)
Velocity (v)	7.85 cm/s (MAXIMUM)	0 cm/s (Momentarily at Rest)
Restoring Force / Accel (a)	0 cm/s² (Zero Net Force)	12.34 cm/s² (MAXIMUM toward Mean)

Step-by-Step Mathematical Calculations

Class 9 Physics (Sindh & Karachi Textbook Board Curriculum)

Step 1[Hz]

Calculate Frequency (f)

f = \frac{1}{T}

Sub: f = \frac{1}{4}

Result:0.25 Hz

Step 2[rad/s]

Calculate Angular Frequency (ω)

\omega = \frac{2\pi}{T} = 2\pi f

Sub: \omega = \frac{2 \times 3.1416}{4}

Result:1.571 rad/s

Step 3[cm]

Displacement Equation of Motion

x(t) = A \cos(\omega t)

Sub: x(t) = 5 \cos(1.57 t)

Result:x(t) \text{ in [}-5, +5\text{] cm} cm

Step 4[cm/s]

Maximum Velocity at Mean Position (v_max)

v_{max} = A\omega

Sub: v_{max} = 5 \times 1.571

Result:7.85 cm/s

Step 5[cm/s²]

Maximum Restoring Acceleration at Extremes (a_max)

a_{max} = \omega^2 A

Sub: a_{max} = (1.571)^2 \times 5

Result:12.34 cm/s²

Class 9 Board Definitions: Simple Harmonic Motion (SHM)

Definition of SHM: To-and-fro periodic motion about a mean position such that acceleration is directly proportional to displacement and is always directed towards the mean position: a ∝ -x.
Time Period (T): Time required by the vibrating body to complete one full cycle (oscillation). Unit: seconds (s).
Frequency (f): Number of complete cycles executed per second (f = 1/T). Unit: Hertz (Hz).
Amplitude (A): Maximum displacement of the oscillating body on either side from its mean position.

Board Numerical Practice & Challenges

Class 9 Karachi/Sindh Board SHM questions with instant simulation verification.

Calculate Frequency from Period

Past Paper: Karachi Board 2023

A simple harmonic oscillator has a time period of T = 4.0 seconds. Calculate its frequency f in Hertz (Hz).

Syllabus Mapping & Learning Objectives

This interactive tool is modeled directly after the official Pakistani textbook curriculam (Sindh Textbook Board, Federal Board Islamabad, and Punjab Textbook Board). It provides live parameter tuning so students can test hypotheses, predict exam outcomes, and observe physical/chemical laws mathematically.

Key Topics Covered

OscillationsSHMWavesSpring

More Study Resources

Pair this simulation with verified solved board past papers and chapter revision notes.

Solved Board Past Papers Chapter-Wise Revision Guides Online Scientific Calculator