A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems? A. The period of the pendulum would increase but the period of the spring would stay the same. B. The period of the pendulum would decrease but the period of the spring would stay the same. C. Both periods would remain the same. D. Both periods would decrease. E. Both periods would increase.

Question

Leonel Manning

Physics

18 February, 08:08

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems? A. The period of the pendulum would increase but the period of the spring would stay the same. B. The period of the pendulum would decrease but the period of the spring would stay the same. C. Both periods would remain the same. D. Both periods would decrease. E. Both periods would increase.

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Answers (1)

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String Bean · Answer 1

A. The period of the pendulum would increase but the period of the spring would stay the same.

Explanation:

Since the elevator accelerates downward uniformly we can use the equation for the pendulum:

T = 2π*√ (L / (g - a))

(g - a) < g ⇒ T (at rest) < T (with constant acceleration downward)

we can say that the period of the pendulum would increase.

The period for a ideal spring can be obtained using the formula

T = 2π*√ (m / k)

which does not depends on the acceleration, then the period of the spring will stay the same.