(1) Compare the Period equation governing the motion and the general equation for a straight line to explain why the graph you made will in fact be a straight line. Use this comparison to show what the value of the slope should be in terms of "g" and "r". What should the y-intercept of your graph be? L T=2π - g -Period equation y = mx + c General equation Periods of Oscillation for Different lengths Period Squared (2) 3.5 2.5 1.5 0.5 1 2 3 0 ò 0.4 0.5 0.6 0.7 0.8 0.9 Pendulum Length (m)
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University Physics 1 - Gravitation & Oscillation
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A Simple Pendulum Lab (Image shown below)
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- What is the frequency of the given oscillation, in Hz? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.You may also recall that for a simple pendulum N = V, where g is the acceleration due to gravity and L is the length of the pendulum. This has been inserted in Equation 4 above. Lastly, this means that angular position 0 of the pendulum is given by: 0 = 0, cos(Nt) Equation 5 Question 1 Use the information above and Equation 2 to write an equation for the period of the pendulum in terms of g and L.Drag each label to the correct location on the equation. Not all labels will be used. The time, 7. in seconds, a pendulum takes to move back and forth once is 2/7 times the square root of the length of the pendulum, L. in feet, divided by the square root of the acceleration due to gravity. 32 feet/second². Enter the correct values in the equation with respect to the motion of the pendulum. 207 T 32 L 882 7.29 0.55 If it takes the pendulum 1.5 seconds to move back and forth once, the length of the pendulum is approximately feet.
- A block attached to a vertical spring oscillates up and down, the length of a spring is shown below. The mass of the block is 5.0 kg. What is the spring constant of the spring, in N/m? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. L (m) 1.4 1.2 1.0- 0.8- 0.6 0.4 0.2 - 0.0 t (s) 6. 3.The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the table to the right. a. Find the least squares line equation and graph it simultaneously with the data points, with L as the horizontal axis and T as the vertical axis. Does it seem to fit the data? b. Find the correlation coefficient and interpret it. Does it confirm your answer to part a? L (ft) T (sec) 1.0 1.13 1.5 1.36 2.0 1.57 2.5 1.76 3.0 1.92 3.5 2.08 4.0 2.22Using a stopwatch, you measure the period of a grandfather clock. Your results are 0.6, 0.6 and 0.7 sec. c. What is your best estimate of the error? d. What is your percent error? e. What is your fractional error? f. Write down your measurement for the period, and express the error in terms of ±.
- Required information The period T of a simple pendulum is given by T = 2√ L/g where L is the length of the pendulum and g is the acceleration due to gravity. Assume g = 9.80 m/s² exactly and that L = 0.742 ± 0.003 m. Estimate T, and find the uncertainty in the estimate. Use pi = 3.1416. The estimated period is s. (Round the final answer to five decimal places.) The uncertainty in the period estimate is s. (Round the final answer to six decimal places.)A pendulum is released and swings until it stops. If it passes through an arc of 25 inches the first pass, and if on each successive pass it travels 2/5 the distance of the preceding pass, how far will it travel before stopping? To solve this problem fully, respond the following questions a) Write the distance traveled in expanded form b) Write the distance traveled in sigma notation c) How far will it travel before stopping?Problem 2 only, read and see the figure, solve carefully, include the units in every step and draw the diagram. Thanks!
- Oscillation Answer = find the periodA weight attached to a spring is pulled down 2 inches below the equilibrium position. Complete parts (a) and (b) below. (a) Assuming the period is 5 second, determine a trigonometric model that gives the position of the weight at time t seconds. s(t) = (Simplify your answer. Type an exact answer, using as needed.) (b) What is the frequency? The frequency is oscillations per sec. (Simplify your answer.)Consider a pendulum whose length is 22 ft. What is the formula for the period of oscillation for a pendulum? (Use the following as necessary: L for the length of the pendulum and g for the acceleration of gravity. Do not substitute numerical values; use variables only.) T = 2√ Determine the period in s. 4.4 x Your response differs from the correct answer by more than 10%. Double check your calculations. s What is the formula that shows the relationship between the natural frequency and the period of oscillation? (Use the following as necessary: T. Do not substitute numerical values; use variables only.) f = Determine the natural frequency in Hz. 0.227 Your response differs from the correct answer by more than 10%. Double check your calculations. Hz