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.