Lab 10: Simple Harmonic Motion University of Michigan Physics Department Mechanics and Sound Intro Labs

This week you move away from rotational motion and begin to study simple harmonic motion. We say that you move away from rotational motion only in the sense that you will not be studying rotating objects as the main focus of the lab. However, it is worth noting that several concepts from rotational motion can be related to simple harmonic motion. You will study three simple harmonic oscillators today: the mass and spring system, the simple pendulum, and the ball and dish oscillator. ^ The projection of rotational motion onto the x or y axis oscillates in simple harmonic motion.

Simple harmonic motion occurs when an object experiences a restoring force proportional to its displacement away from some equilibrium position that acts towards the equilibrium position, or in the form of an equation, F=-kx. You will see in your lab manual that the equation of motion for simple harmonic oscillators has the form x(t) = A sin(ωt +δ). You will investigate today how ‘ω’ arises as a natural property of the oscillating system independent of the amplitude of the motion.  Various pendulum bobs that you will use today. You will investigate the dependence of frequency based on physical properties such as mass and length of the pendulum.

Your experimental apparatus today is a photogate paired with various oscillating systems. The photogate records the time at which its beam is broken, from which you can calculate the period of the oscillation. Notice that the time between two successive photogate signals is only half of the period.  The ball in a dish set up that you will use in this lab. You can see that the photogate for this apparatus is already attached.

You will need to adjust the photogate height throughout the lab, as you will be measuring the period of springs with different spring constants and pendulums of different lengths. You will use the orange clamp at the top of the large stand to hold your spring or string. To take data, just displace the object slightly from its equilibrium position and click ‘collect’ on LoggerPro ®.  A sample mass and spring set up. You will need to adjust the photogate height using the lower clamp on the stand.

After today’s lab you will have a better understanding of simple harmonic motion. You should see that simple harmonic oscillators can be described by one equation of motion, and also that their frequency of oscillation is a natural function of the properties of the oscillator. Your understanding of simple harmonic motion will be helpful for next week’s investigation of wave motion and sounds.  A typical pendulum set up for this lab.