Distance measurement using HY-SR04 Piezo sensor

HY-SR04 is a widely available ultrasound ranging module. It consists of two 40 kHz Piezo crystals, one acts as a transmitter and other as a receiver, and some electronics circuitry to measure the time interval between a burst of sound transmitted and the echo received.
The four pins are the power supply, ground, trigger and Echo. This module can be connected to ExpEYES-17  as shown in the schematic, to measure distance between the module and the reflecting surface, with an error less than 3mm. This can be used to design several experiments in mechanics.

The Mass and Spring problem

When a mass suspended on a spring is made to oscillate, the period of oscillation is given by  T = 2 * pi * sqrt( m/k), where m is the mass and k is the spring constant. We can measure the period of oscillation by measuring the distance to the moving mass as a function of time. The distance versus time graph is fitted with a sine function to calculate the frequency. The photograph below shows a metal plate suspended on a spring and the SR04 facing it from the bottom. The distance to the oscillating plate is measured for 5 seconds and the data is fitted to a sine function.

A video of the experiment is HERE.

Simple Pendulum

     The period of oscillations of a pendulum also can be measured using SR04 connected to ExpEYES. The figure shows a pendulum with a rectangular bob, but one can use a spherical bob with a piece of paper (to provide a flat reflecting surface) pasted to it. The measured frequency is 1.05 Hz for a pendulum having a length of 22cm. One can calculate the value of acceleration due to gravity from this data.

A video is HERE.

Free Fall, Displacement as a function of Time

It is possible to measure the distance to a body falling under gravity. The value of 'g' can be calculated by fitting the data with the polynomial
S(t)= a * t^2 + b * t + c
'g' is given by 2*a