PCS-125-Lab 1 (2)

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McMaster University *

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2B03

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Physics

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Apr 3, 2024

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Pre Lab Questions: 1. ? = ? ? If the amplitude is varied it will have no effect on the angular frequency. If the mass is increased then the angular frequency will become smaller, if the mass is decreased then the angular frequency will become bigger. If the spring constant is increased then the angular frequency will also increase, if the spring constant is decreased then the angular frequency will decrease. This is due to the angular frequency equation .

2.In order to determine the spring constant I would plot the frequency as the y axis and the mass as the x axis. Calculating the slope of that graph should yield the spring constant. Introductions: The objective of this lab is to see how the period of oscillations changes when changes are made to a spring-mass system the secondary object of this lab is to try and determine the spring constant from the data collected. In the first experiment, the spring constant and the mass both will stay fixed and the amplitude of the spring-mass system will change, the period of oscillation will be observed and recorded as the amplitude is changed. In the second experiment, the amplitude and the spring constant will both stay fixed and the mass of the spring-mass system will be changed. Again the period will be observed and recorded as the mass changes. In the third experiment, the spring constant will be fixed and the mass of the spring-mass system will be changed. The displacement of the spring will be recorded as the mass changes, this displacement will be used to calculate the spring constant later on. Theory:

In the lab the main equation used was ( . This equation shows how the period of an 𝑇 = 2π ? ? ) object in simple harmonic motions changes when the mass and the spring constant are changed. The derivation of this equation is shown below. It is known that to describe and understand simple harmonic motion this equation is used. ???𝑎?𝑖?? 1: ?(?) = 𝐴𝑐??(?? + Φ) It is also known that since cos(x) is a periodic function then the following equation is true. ???𝑎?𝑖?? 2: 𝑐??(?) = 𝑐??(? + 2π) Combining equation 2 and 3 will allow us to derive the period equation. ???𝑎?𝑖?? 3 : 𝐴𝑐??(?? + Φ) = 𝐴𝑐??(?(? + 𝑇) + Φ) ???𝑎?𝑖?? 4: ? = ?? + Φ ???𝑎?𝑖?? 5: 𝑐??(?? + Φ) = 𝑐??(?? + ?? + Φ) Sub equation 4 into equation 5 Equation 6: 𝑐??(?) = 𝑐??(? + ?𝑇) Comparing equation 6 and 2 we can see that ?𝑇 = 2π Simply solve for T and we get the period equation to be 𝑇 = 2π ? = 2π ? ? I predict that for experiment one the period will not change since in experiment one the only thing that we are changing is the amplitude and as seen from the equation the amplitude will not affect the period. In experiment two I predict that the period will increase as the mass increases. And for the third experiment, I predict that the displacement will increase as the mass increases. Producer: Experiment 1:

Step 1: Make sure that the damping is set to zero, the gravity is set to 9.8m/s^2, the spring constant is set to the second increment and the mass is set to 50g. Step 2: Place the mass on the spring and use the ruler tool and line it up so the zero is at the start of the mass. Step 3: Make sure the simulation is stopped and pull down the mass to the desired amplitude. Step 4: Start the simulation and use the timer tool to record 10 oscillations and do this three times. Step 5: Take the average for the three trials and divide by 10 to get the desired period. Step 6: Change the amplitude and repeat steps 4 and 5 Experiment 2: Step 1: Make sure that the damping is set to zero, the gravity is set to 9.8m/s^2 and the spring constant is set to the second increment. Step 2: Place the mass on the spring and set the amplitude to 0.2 meters Step 3: Start the simulation and use the timer tool to record 10 oscillations and do this three times Step 4: Take the average for the three trials and divide by 10 to get the desired period. Step 5: Use 5 more different masses and repeat steps 3 and 4 Experiment 3: Step 1: Make sure that the damping is set to zero, the gravity is set to 9.8m/s^2 and the spring constant is set to the second increment. Step 2: With no mass on the spring take the ruler tool and place it so the zero end of the ruler is at the end of the spring

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