## Period of a spring (SHM)

Practical Activity for 16-19

In this activity students use the phyphox app to determine the spring constant, *k*, using a mass-spring system.

#### Equipment

- A phone with phyphox installed
- A mass balance
- A set of springs
- A set of masses
- A clamp and clamp stand
- A tight elastic band or homemade holder

#### Preparation

Make sure the phones have protective cases to protect them should students accidentally drop their phones.

Consider pairing or grouping students to ensure each student has access to a device with the “spring” function. This can be checked in the phyphox app (if it doesn’t have the “spring” function it will be greyed out).

#### Instructions

Ask students to:

- Open the phyphox app and click on “Spring”.
- Record the mass of the phone in kg.
- Suspend the spring from a clamp and attach the phone securely to the bottom of the spring (e.g., using a tight elastic band wrapped around the midline of the phone) and secure the stand so that it does not move as the phone and spring oscillate (either clamp the stand or put a large mass on the base).
- Pull the phone vertically downwards a few centimetres, press play and release.
- Make a note of the period once the oscillations have settled, which takes approximately 15 seconds.
- Suspend a 50 g mass from the bottom of the phone.
- Repeat steps 3-4 adding 50 g each time up to 300 g.
- Plot a straight-line graph to determine the spring constant,
*k*.

#### Teaching notes

If students are unfamiliar with the relationship for the period *T* of a spring introduce it:

*T* = 2π *m**k*

They can determine *k* by plotting *T*^{ 2} against *m*, where each value of *m* is the mass of the phone plus the standardised mass set the students are using. The gradient of the straight-line graph will be equal to *4π*^{ 2}/*k*. The line of best fit should pass through the origin.

The results should look similar to to the graph below:

As an extension activity, students can investigate adding more springs in series and/or parallel to see how this changes the period and effective spring constant.

#### Learning outcome

Students describe an experiment to determine the spring constant of a spring.