How do we understand motion that repeats in cycles?
A pendulum and a mass on a spring are both good examples of oscillators, or systems that exhibit repetitive behavior. This investigation looks at how motion characteristics such as period and frequency are affected by physical variables such as mass, length, and spring constant.
Part 1: Period of a pendulum
Assemble the pendulum as shown, with 5 washers on the mass hanger.
Set the pendulum swinging and observe the motion. Do not let the swinging mass hanger hit the stand.
Hold the angle indicator behind the string to measure the amplitude of the motion.
With a stopwatch, measure the time it takes to complete 10 full cycles.
Change the amplitude, mass, and string length and see how each variable affects the period of your pendulum. Tabulate your data.
Describe how you determined one full cycle of the pendulum.
How does the period of the pendulum depend on length, mass, and amplitude? Support your answers using the data.
Propose a design for a pendulum that has a period of 2.0 s.
How did you choose the number of trials for each variable?
Part 2: Mass and spring oscillator
Set 6 washers on the mass hanger. Attach the mass and stiff spring. Place the meter rule against the stand. Note the position of the top washer in its equilibrium position.
Displace the mass 5 cm and release it. Record the time to complete 10 oscillations.
Repeat the experiment and record data for different masses and amplitudes.
Replace the stiff spring with the medium spring (different spring constant) and set 6 washers on the mass hanger.
With a stopwatch, measure and record the time to complete 10 oscillations.
With a spring scale, measure and record the force needed to extend each spring 10 cm. Calculate the spring constants. The spring constant is k = F/x where F is in newtons and x is in meters.
How did you determine one full cycle of the motion?
How does the period of the mass/spring oscillator depend on mass and amplitude? Your answer should be supported by the data.
Explain the answer to part (b) using Newton's second law, F = ma.
How does the period of the mass/spring oscillator depend on the spring constant? Your answer should be supported by the data.
In step #3 above, what were the independent, dependent, and controlled variables?
Use this electronic utility as a stopwatch to time the pendulum oscillations.