Question

Now, for parts F-I, you will investigate how the period of oscillation depends on the properties of the pendulum. The period of oscillation is the amount of time it takes for the pendulum to take a full swing, going from the original angle to the other side, and returning to the original angle. You can determine the period by selecting other tools, which gives you a stopwatch. With the pendulum swinging, you can start the stopwatch when the pendulum is at its original angle and time how long it takes to complete 10 swings. The period will be this time interval divided by 10 (this method is more accurate than trying to time one swing). Set the length of the pendulum to 1.0 m and the mass to 1.0 kg. Click Reset, and then drag the pendulum to an angle (with respect to the vertical) of 30∘ and release it. What is the period of oscillation?

a. 1.0 s
b. 1.58 s
c. 20.0 s
d. 2.0 s
e. 0.5 s

Answer 1

Using the formula for the period of a simple pendulum T = 2π √(l/g), where l is 1.0 m and g is approximately 9.8 m/s², the period for one oscillation is approximately 2.0 seconds. Therefore, the correct answer to the question regarding the period of oscillation for a pendulum with a 1.0 m string length would be choice d.

Step-by-step explanation:

The period of a simple pendulum, like the one described in the question, depends only on the length of the string and the acceleration due to gravity. The formula for the period T of a pendulum is T = 2π √(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. Mass and amplitude, provided the latter is small, do not affect the period. Given that the length l is set to 1.0 m, and assuming the standard acceleration due to gravity g is approximately 9.8 m/s², the theoretical period is approximately 2π √(1.0 m / 9.8 m/s²), or approximately 2π √(0.102 s²), which calculates to around 2.0 seconds for a full swing. Therefore, if a student times 10 swings and divides the total time by 10, the resulting period should be approximately 2.0 seconds per swing, which corresponds to answer choice d.