Question

In cases where the restoring force is proportional to the amount of displacement from the oquilibrium position, the object undergoes simple harmonic motion (SHM). An object on a spring is the simplest example of SHM because the force generated by a spring is proportional to how much the spring is stretched: = -67 (1) where k is the spring constant, and x is the distance the object has been displaced from equilibrium. Note the negative sign in Equation 1, indicating that the force generated by the spring is always in the opposite direction of the displacement from equilibrium; thus, the spring force is a restoring force. Equation 1 is Hooke's Law, which holds as long as the displacements from cquilibrium are not too large and works well for describing springs but also molecules in a solid that have spring like bonds holding them to their neighbors like that pictured at right. From this theory, it can be shown that the frequency of oscillation f for an object of mass m undergoing simple harmonic motion is W000203 f 1 2x m Learning Goals for this Lab: Understand what frequency, period, and amplitude are, and how to extract them from graphs of sinusoidal motion. Understand what kind of force can generate periodic motion. Practice comparing theoretical prediction and experimental results. Part I Frequency vs. amplitude Nowhere in Equation 2 is amplitude included. Is it really true that imparting a large amplitude vibration doesn't affect the frequency of the oscillation? For Part I, let's test the hypothesis that frequency is independent of the amplitude of motion. The videos provided show a 50 g mass on a spring that is made to oscillate with either a small amplitude, medium amplitude, or large amplitude. Your task is to analyze the videos and report whether your results support or refute the hypothesis. You must report the procedure you use including the steps you took to analyze the data. Be sure to include graphs and fits in your report to support your conclusions.

For my lab a 50g mass is on a spring. The spring is pulled down a different length for each trial and then released. What would the amplitude of motion be for this experiment and how can I test that the frequency is independent from the amplitude.

Answer 1

h, from Time one X₂ let stretch the spring x, from equilibrium position. then release and note the period of oscillation. again repeat experiment for stretching spring i from equilibrium. position and note the Time period again of oscillation. time period same case for different Amplitudes at Cx, ; X₂ , ....). frequency = f ( Time period ) You will get frequency is independent of Amplitude. in each You will get the amd so,