## Period of Simple Harmonic Oscillations

#### Purpose

To measure the period of oscillations of a spring and determine its stiffness.

**Objectives**

To learn how to measure the period of an oscillating spring.

To learn how to improve the accuracy of experimental results by avoiding measuring small quantities, and by measuring repetitively the same quantities.

To learn how to use spreadsheets for inputting formulae and performing calculations.

**Equipment**

- Springs, a hook, and weights
- Meterstick
- Mass Scales
- Timer

#### Theory

When a block with mass *M* hangs on a spring with stiffness *k*, it will oscillate with a period *T *given by the following formula:

*T* = 2 π √ (*M*) ⁄ (*k*) (Eq. 1)

#### Experimental Setup

Using a clamp, set a spring to hang vertically from the rod. Place 150 g to a 50-g hook and hang everything on the spring. The total mass now will be 200 g, or 0.20 kg

#### Measurements

The period of oscillations is very close to 1 second and it is difficult to measure it with great accuracy. So, measure the time for 20 oscillations, *t*, and calculate the period *T*:

*T = **t / 20 *(Eq. 2)

Since the spring has its own mass, as well, that will affect the period. In order to account for that effect, you need to measure the mass of the spring and add one third of it to the total mass. Thus the effective mass for the Eq. 1 will be:

*M _{eff } = M + (1/3) M_{spring}* (Eq. 3)

#### Results

Determine the spring stiffness *k*.

#### Questions

*Does the value for the spring stiffness agree with the value you determined in the previous lab Springs I?*