A pendulum on Planet X, where the value of m is unknown, oscillates with a period T1 = 8 s. Note that you do not know the value of m, L, or g, so do not assume any specific values. The required analysis involves thinking about ratios.

(A) What is the period of this pendulum if its mass is doubled? Express your answer with the appropriate units.

(B) Its length is doubled? Express your answer with the appropriate units.

(C) Its oscillation amplitude is doubled? Express your answer with the appropriate units.

Question

Physics

Marissa

28 January, 03:20

A pendulum on Planet X, where the value of m is unknown, oscillates with a period T1 = 8 s. Note that you do not know the value of m, L, or g, so do not assume any specific values. The required analysis involves thinking about ratios.

(A) What is the period of this pendulum if its mass is doubled? Express your answer with the appropriate units.

(B) Its length is doubled? Express your answer with the appropriate units.

(C) Its oscillation amplitude is doubled? Express your answer with the appropriate units.

+5

Answers (1)

Know the Answer?

Felipe Baker · Answer 1

Given:

T1 = 8 s

For a simple harmonic motion, period, T = 2pi * sqrt (L/g)

A.

M2 = 2 * M1

The period is not dependent on mass.

T = 2pi * sqrt (L/g)

T1 = T2 = 8 s

B.

L2 = 2 * L1

T = 2pi * sqrt (L/g)

L1/T1^2 = L2/T2^2

T2 = sqrt ((2 * L1 * 64) / L1)

= sqrt (128)

= 11.314 s

C.

Period is independent on the amplitude of the oscillation. T1 = T2 = 8 s