A pendulum has length 0.22 meter. A bob is released from rest from a starting angle . Find an equation for the position at any time t and find the amplitude and period of the motion. [The acceleration due to gravity is 9.8 m s^-2.] A) amplitude: 0.2 m; period: 0.941 rad B) amplitude: 0.2 m; period: 0.471 rad C) amplitude: 0.4 m; period: 0.471 rad D) amplitude: 0.4 m; period: 0.941 rad

Question

Quizplus · Accepted Answer

The equation for the position at any time t for a pendulum is given by:

θ = θ0 cos(ωt)

where θ0 is the amplitude, ω is the angular frequency, and t is time.

To find the amplitude, we need to first find the maximum angle that the bob swings from the vertical. Using the starting angle and the length of the pendulum:

L cos(θ0) = L - 0.22 = -0.22

cos(θ0) = (-0.22)/L = -1

This means that the maximum angle is θ0 = π/2 radians or 90 degrees. Therefore, the amplitude is 0.22 m sin(π/2) = 0.22 m.

To find the period, we can use the equation:

T = 2π √(L/g)

where g is the acceleration due to gravity. Plugging in the given values:

T = 2π √(0.22/9.8) = 0.941 seconds

Therefore, the correct answer is D) amplitude: 0.4 m; period: 0.941 rad.

A Pendulum Has Length 0