An air track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 seconds. It then oscillates wit

Question

An air track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 seconds. It then oscillates with a period of 2.40s and a maximum speed of 30.0 cm/s. What is the glider’s position at t=0.300s?

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Ladonna 5 months 2021-08-04T07:14:35+00:00 1 Answers 15 views 0

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    2021-08-04T07:16:12+00:00

    Answer:

    The glider’s position at t=0.300s is 8.1 cm

    Explanation:

    Given;

    maximum speed of the glider, v_{max} = 30.0 cm/s = 0.3 m/s

    period of the oscillation, T = 2.4 s

    Maximum speed of oscillation is given by;

    v_{max}  = ωA

    Where;

    A is the amplitude of the oscillation

    ω is the angular speed

    \omega = \frac{2\pi}{T} \\\\\omega =\frac{2\pi}{2.4}\\\\ \omega = 0.833 \pi

    The amplitude of the oscillation is given by;

    A = \frac{v_{max}}{\omega} \\\\ A = \frac{0.3}{0.833\pi}\\\\ A = 0.1146 \ m

    The position of the particle is given by;

    x(t) = A cosωt

    x(0.3) = (0.1146)cos(0.833π x 0.3)

    x(0.3) = (0.1146)cos(0.833π x 0.3)

    x(0.3) = (0.1146)cos(45)

    x(0.3) = 0.081 m

    x(0.3) = 8.1 cm

    Therefore, the glider’s position at t=0.300s is 8.1 cm

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