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Usually the load will be much greater than that of the spring ($m \gg \mu$), so $\mu$ could be ignored. Since $\omega^2 = \dfrac{k}{m}$ and $T = \dfrac{1}{f}$, then $$T = 2\pi \sqrt{\frac{m}{k}}$$, The equation of motion for a simple harmonic oscillator,is. I did a lab with a mass attached to a vertical spring. Disclosure: As an Amazon Associate I earn from qualifying purchases. You add a linear fit and find the following equation of the line: y=8.25x-0.065 What is the spring constant, k (in N/m or kg/s2) Rating: 4.1 / 5. You perform the Simple Harmonic Motion experiment and create a plot of Period-Squared vs. Mass. Calculate the time period of the oscillation." If you do not know $\mu$ then simply plot $T^2$ against load $m$. The obtained value of C is 0.694, which is closest to 1/3. Is ground connection in home electrical system really necessary? "A mass of $10$ kg bounces up and down on a spring. How to find the value for the spring constant from the graph of period against the square root of mass. [closed]. We have placed cookies on your device to help make this website better. The starting position of the spring was recorded using a stretch indicator. For a better experience, please enable JavaScript in your browser before proceeding. physics classical-mechanics. What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? Sorry. The natural resonant frequency of the oscillator can be changed by changing either the spring constant or the oscillating mass. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Calculating time period of oscillation of a mass on a spring [closed], “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, Oscillation and Damped oscillation program, Calculating velocity of mass at equilibrium, Finding amplitude of oscillation without graph. So plot the period squared versus the mass. $$ From these data, a graph of force versus displacement was plotted, and a linear fit slope revealed the spring constant. Paul J. Angiolillo (Teacher) / PHY 1042 (General Physics Lab II) (Class) / Saint Joseph’s University (School) / schoolwork (Post Type). Finding the slope and intercept of a graph, Using the slope of the graph, write an equation for this proportion, Measuring the strength of the earths magnetic feild using the slope of a graph. But problem is you dont know how to plot the line more precisely. During part two of the experiment, the period of the spring was measured as amplitude changed while mass remained constant. This was not surprising considering the given equations. The square of the period versus mass for each trial was plotted and a linear fit was taken. In Monopoly, if your Community Chest card reads "Go back to ...." , do you move forward or backward? Calculate time constant from the slope of dimensionless temperature vs time graph. As the mass was increased, the period also increased. The units of 1/slope are. The formula $T^2=4\pi^2 \frac{m}{k}$ assumes that the spring is ideal and has no mass. The unit of angular frequency is . Period squared vs mass lHang a 200.0Bmass from the spring. Is ground connection in home electrical system really necessary? The spring constant is in units of force per unit displacement, N/cm. ADAM CAP is an elastic waistband enthusiast, hammock admirer, and rare dingus collector hailing from Berwyn, Pennsylvania. How would my graph of T2 vs mass change if the spring constant was doubled. For a spring, we know that $F=-kx$, where $k$ is the spring constant. T predicted using the first equation and M = 1.000 kg is 3.24 s. T predicted using the second equation and M = 1.000 kg is 3.26 s. This is a percent difference of only 0.615%. Does it include the mass of the spring? The graph of $T^2$ vs load $m$ is linear but if $\mu$ is not negligible compared with loads $m$ then $T^2$ will not be proportional to $m$. I as study simple harmonic motion and I am using this equation: Period =2pi * square root * (mass/spring constant). This was not surprising considering the given equations. $\mu$ contributes to the total inertia which is oscillating and should therefore be added to the load $m$ when you use the formula. T predicted using the first equation and M = 0.050 kg is 0.726 s. T predicted using the second equation and M = 0.050 kg is 0.771 s. This is a percent difference of 6.01%. Does a DHCP server really check for conflicts using "ping"? lUse the stopwatch to time 10oscillations and record this time in Table 2. lHave your partner repeat the timing of 10oscillations and record the result in Table 2. dmja, October 16, 2010 in Homework Help. Maximum acceleration of mass at the end of a spring, Probability density function of harmonic oscillation, What's is the purpose of a trailing '-' in a Kubernetes apply -f -. Consider the value you obtained for C. If you were to express C as a whole number fraction, which of the following would best fit your data (1/2, 1/3, 1/4, 1/5)? After graphing forces versus displacement, a value of 3.53 N/m was determined as the spring constant. Whoa! It would mean that you would get every time new $T$ for same mass $m$ and spring $k$. From the laws of Simple Harmonic Motion, we deduce that the period $T$ is equal to: Therefore, we substitute $m=10$ and $k=250$ to obtain the solution: $$T={2\pi}{\sqrt{\frac{10}{250}}}={2\pi}{\sqrt{\frac{1}{25}}}={2\pi}{\frac{1}{5}}=\frac{2\pi}{5}$$, Note $f = \dfrac{\omega}{2\pi}$, where $\omega$ is the angular frequency.

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