Vernier Software and Technology
Vernier Software & Technology

Simple Harmonic Motion: Mathematical Model

Figure from experiment 15 from Advanced Physics with Vernier — Mechanics


When you suspend an object from a spring, the spring will stretch. If you pull on the object and release it, it will begin to oscillate up and down. In this experiment, you will examine this kind of motion, perform a curve fit on the position-time graph, and relate the parameters of the equation with physical features of the system.


In this experiment, you will

  • Collect position vs. time data as a mass, hanging from a spring, is set in an oscillating motion.
  • Determine the best fit equation for the position vs. time graph of an object undergoing simple harmonic motion (SHM).
  • Define the terms amplitude, offset, phase shift, period and angular frequency in the context of SHM.
  • Relate the parameters in the best-fit equation for a position vs. time graph to their physical counterparts in the system.
  • Use deductive reasoning to predict the system mass required to produce a given value of angular frequency in the curve fit to SHM.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Advanced Physics with Vernier — Mechanics

See other experiments from the lab book.

1Motion on an Incline
2Error Analysis
3Newton's First Law
4Newton's Second Law
5Newton's Third Law
6Projectile Motion
7Energy Storage and Transfer: Elastic Energy
8Energy Storage and Transfer: Kinetic Energy
9Energy Storage and Transfer: Gravitational Energy
10AImpulse and Momentum (Motion Detector)
10BImpulse and Momentum (Photogate)
11AMomentum and Collisions (Motion Detectors)
11BMomentum and Collisions (Photogates)
12ACentripetal Acceleration
12BCentripetal Acceleration
13Rotational Dynamics
14Conservation of Angular Momentum
15Simple Harmonic Motion: Mathematical Model
16Simple Harmonic Motion: Kinematics and Dynamics
17Pendulum Periods
18Physical Pendulum
19Center of Mass

Experiment 15 from Advanced Physics with Vernier — Mechanics Lab Book

<i>Advanced Physics with Vernier — Mechanics</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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