This experiment has much in common with the investigation we did earlier of the period of oscillation of a mass on a pendulum. After completing the pre-lab exercises, list at least 3 assumptions we will likely make for the mass on a spring experiment.
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Answer:
The purpose of this lab is to measure the period of a simple pendulum, and experimentally determine the relationship between the period T and the length L of a pendulum. You will also begin to learn how to find, investigate, and understand major sources of uncertainty and error in measured and calculated quantities.A simple pendulum consists of a mass m (ideally, concentrated to a single point) having gravitational weight (a vector) w⃗ =mg⃗ , suspended from a fixed point by a string (ideally, massless) of length L. (For your convenience, the figure below also shows the two components of w⃗ , one parallel to the string and one perpendicular to the string.) If carefully set into motion, the mass swings along an arc (labeled by S) lying in a plane that contains the gravity vector g⃗ . θ(t) is the time-dependent angle that the taut string makes relative to the vertical, defined by the direction of g⃗ . If the mass is NOT carefully set into motion, it becomes a conical pendulum, which does not swing along a vertical plane and is, therefore, a more complicated physical system. For the purposes of this experiment, you will need to ensure that your simple pendulum swings in a vertical plane.
The “period” of this motion is defined as the time T needed for the mass to swing back and forth once. We will see, later in this course, that the approximate relation between the period T and length L of a simple pendulum is T=2πLg−−√, where the magnitude of g is 9.81 m/s2. In the derivation of this equation, the assumption is made that the angle θ is small, so that sin(θ)≈θ (where θ is measured in radians).
By measuring the period T of oscillation of the pendulum as a function of the length L of the string, you can experimentally determine an estimate for the value of g, the acceleration due to gravity. The different quantities that are important within this experiment are T, L, and θ. Note that to minimize random errors, you should measure L several times and the time it takes for 10 oscillations rather than just one oscillation. By taking an average value, you will reduce the effects of making a single unusually high or low measurement.
If the computer at your lab table has the program SnapTimePro installed, accessible via the Desktop icon labeled “Shortcut to SnapTimePro,” then use it as your timer. If not, use a stopwatch.
For this experiment, you will conduct two analyses: one of the effect of angle θ on period T, and one of the effect of string length L on period T.
Explanation:
I hope this has been helpful for you.