A simple pendulum consists of a mass m (the "bob") hanging on the end of a thin string of length l and negligible mass. The bob is pulled sideways so the string makes a 5.0° angle to the vertical; when released, it oscillates back and forth at a frequency f. If the pendulum is started at a 10.0° angle instead, its frequency would be (a) twice as great. (b) half as great. (c) the same, or very close to it (d) not quite twice as great. (e) a bit more than half as great.

Question

Jacqueline Phelps

Physics

9 June, 01:45

A simple pendulum consists of a mass m (the "bob") hanging on the end of a thin string of length l and negligible mass. The bob is pulled sideways so the string makes a 5.0° angle to the vertical; when released, it oscillates back and forth at a frequency f. If the pendulum is started at a 10.0° angle instead, its frequency would be (a) twice as great. (b) half as great. (c) the same, or very close to it (d) not quite twice as great. (e) a bit more than half as great.

+3

Answers (1)

Know the Answer?

Journey Conway · Answer 1

The pendulum frequency is (c) the same, or very close to it

Explanation:

The simple pendulum corresponds to a simple harmonic movement, to reach this approximation in the expression of the force the sine of the angle (θ) approaches an angle value, this is only true for small angles, generally less than 15º

Sine (15th) = 0.2588

The angle in radians is 15º π / 180º = 0.26180.2588 / 0.2618

The difference between these two values is less than 1.2%

for smaller angle the difference is reduced more

Therefore, the period for both the 5º and 10º angles is almost the same