27 November 2025

Simple Harmonic Motion – Measuring SHM with PASCO Sensors

Simple Harmonic Motion (SHM) appears all over physics: oscillating springs, swinging pendulums, vibrating masses, tuning forks, air columns, and even molecules in solids. It’s a perfect topic for hands-on investigation, and with PASCO sensors, students can collect precise displacement, velocity, and acceleration data to see SHM unfold in real time.

What Is Simple Harmonic Motion?

An object in SHM experiences a restoring force that is proportional to its displacement and acts towards equilibrium:

F = -kx

This produces motion that is:

periodic,
symmetrical,
and modelled by sine and cosine functions.

PASCO equipment makes these ideas visible and measurable.

Measuring SHM with PASCO Sensors

1. Spring–Mass System (Wireless Motion Sensor or Smart Cart)

Attach a mass to a vertical or horizontal spring.
Start oscillations and use the motion sensor to track displacement.

Data shows:

sinusoidal displacement–time graphs
velocity 90° out of phase
acceleration proportional to –displacement

Students calculate the period:

T = 2\pi \sqrt{\frac{m}{k}}

and verify it experimentally.

Add the Force Sensor to see the effect of force.

2. Simple Pendulum (Motion Sensor or Photogate)

A PASCO rotational sensor or a motion sensor or photogate can track the oscillation period of a small pendulum.
Students test how the period changes with:

length of the string
amplitude (for small angles)

and compare data with:

T = 2\pi\sqrt{\frac{L}{g}}

3. Smart Cart Oscillations on a Track

The PASCO Smart Cart, acting as a mass attached to long springs, provides a clean horizontal SHM system. The Pasco Track is mounted at a steep angle, and the cart is allowed to oscillate, suspended by a spring.

With the track level two, springs can be used, one at the top and the other at the bottom.
Built-in position and acceleration sensors allow simultaneous measurement of:

$x(t)$
$v(t)$
$a(t)$

Graphs clearly show the phase relationships between each.

4. Torsional Oscillator (Rotary Motion Sensor)

Using a rotary motion sensor and a torsion wire, students observe rotational SHM.
They can measure moment of inertia, torsion constant, and compare with:

T = 2\pi\sqrt{\frac{I}{k_\tau}}

This links SHM theory to rotational dynamics.

Why PASCO Makes SHM Clear

Real-time graphs reveal phase differences instantly
Data is smooth and accurate, ideal for curve fitting
Students can test how mass, stiffness, and amplitude affect period
Results link directly to A Level equations and modelling

The combination of hands-on systems and digital sensors helps students understand SHM as both a physical motion and a mathematical model.

Skills Highlight

Collecting and analysing real-time motion data
Using PASCO sensors to measure displacement, velocity, and acceleration
Fitting sinusoidal curves to experimental data
Investigating how system parameters affect oscillation
Linking mathematical models to physical behaviour

Why It Works in Teaching

SHM is everywhere — from clocks and guitars to earthquakes and resonance.
PASCO technology lets students see the full picture:
the forces, the curves, the timing, and the mathematics behind oscillatory systems.

27 November 2025