A(Вm (kg)0.20.40.60.81.0DT (s)2.55+2.400.1T (s)2.462.492.52.512.53A student investigates the effect the mass of the hanging sphere has on the period T of a pendulum'soscillation. Solid lead spheres of varying diameter and mass are used for the pendulum. The studentattaches the spheres to the end of a 1.50 m long string and sets the resulting pendulum into small-angleoscillation, as shown in the figure. A stopwatch is used to measure the time for 10 oscillations, and theperiod is calculated by dividing this value by 10. The resulting data are tabulated in the table and plottedon the graph shown. A linear regression is performed on the data and yields the equationT = (0.08 ) m + 2.45 s. From the evidence, the student concludes that the period of a pendulumincreases linearly with mass. Which of the following statements is the best assessment of the student'sconclusion and provides supporting evidence?1.0m (kg)The results completely support the expected result; the period is expected to increaselinearly with mass.The results partially support the expected result; the period is expected to increase withmass but not linearly.The results do not support the expected result; there is error in the data that has beenmisinterpreted as the period increasing linearly with mass.The results do not support the expected result; the period seems to be increasing wimass, but the effective length of the pendulum is actually increasing as larger bobsattached.OOL

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I am having a hard time finding the meaning of what T2 is in the equation. Do I just square the T or do something else? Thanks for the help in advanced.
For Parts I and II, use the pendulum equation and solve to predict the length needed for a pendulum with a period of 1 s and 2 s respectively. Use a piece of string (or thread, dental floss, shoe lace, etc.) and a steel nut (or washer or something small but with enough mass to weigh down the string) to build each pendulum. Time each pendulum for 30 periods and then find the average time for one period. Remember, a period is the time to complete one cycle of motion, out and back. Tape each pendulum up in perhaps a doorway where it is stationary and has room to swing. Be precise with your measuring and timing. Show your work. Part I Given: T = 1.00 s l =? Part II Given: T = 2.00 s l =?
DONT MIND THE BIG NUMBER ON THE RIGHT, IT IS JUST FOR NUMBERING. MAKE SURE IT IS CORRECT AND TYPEWRITTEN TO GET AN UPVOTE. NO UPVOTE IF IT IS HANDWRITTEN. THANK YOU
Do number 2
You will fire the spring gun 3 times from the first detent and measure the change in height of the (pendulum + ball) for each shot. Write the equation for the change in height of the first shot.
The quantities A and φ (called the amplitude and the phase) are undetermined by the differential equation. They are determined by initial conditions -- specifically, the initial position and the initial velocity -- usually at t = 0, but sometimes at another time. In the oscillating part of the experiment, I measured only the time of 30 periods. I measured no position or velocity. Consequently, A and φ (and also y0) are irrelevant in the problem. We only compare the period T or the frequency ω with the theoretical prediction. You have (hopefully) derived (or maybe looked up) the relation between ω and k and m. This final question relates ω and T. If ω = 8.2*102 rad/s, calculate T in seconds. (Remember, that a radian equals one.) T might be a fraction of a second.
The quantities A and p (called the amplitude and the phase) are undetermined by the differential equation. They are determined by initial conditions -- specifically, the initial position and the initial velocity -- usually at t = 0, but sometimes at another time. In the oscillating part of the experiment, I measured only the time of 30 periods. I measured no position or velocity. Consequently, A and p (and also yo) are irrelevant in the problem. We only compare the period T or the frequency w with the theoretical prediction. You have (hopefully) derived (or maybe looked up) the relation between w and k and m. This final question relates w and T. If w = 5.8*10° rad/s, calculate T in seconds. (Remember, that a radian equals one.) T might be a fraction of a second.