Question

1. For a simple harmonic movement, is it possible that the position, speed and acceleration are at some point in the same direction, or at least two of them are? Explain.

2.If a pendulum is in an elevator, what happens to its period if the elevator a) accelerates upwards, b) moves with constant speed upwards, c) accelerates downwards, d) accelerates downwards with the acceleration of gravity (9.8m/s2)?

Answer 1

1.

Yes, the displacement and velocity can be in the same direction at some point. When a particle in simple harmonic motion is moving from the equilibrium position to the extreme position, the displacement and velocity are in the same direction.

2.

The time period of a pendulum in an elevator is

T = 2π(l/ge)1/2

a)

when the elevator is moving upwards with an acceleration a then the effective acceleration,

ge = g + a

T = 2π(l/g+a)1/2

b)

Where ge is the effective acceleration and l is the length of the pendulum

ge = g = 9.8 m/s2 when the elevator is moving with a constant velocity

time period, T = 2π(l/g)1/2

c)

when the elevator is moving downwards with an acceleration a then the effective acceleration,

ge = g - a

T = 2π(l/g-a)1/2

Given that a = g

T = 2π(l/g-g)1/2 = infinity