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14 December, 22:52

A mass on a spring vibrates horizontally on a smooth level surface. its equation of motion is x (t) = 8 sin (t), where t is in seconds and x in centimeters. find the velocity and acceleration of time. find the position, velocity, and acceleration of the mass at time t=2pi/3. in what direction is it moving at that time

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  1. 15 December, 00:22

    we have given the equation of motion is x (t) = 8sint [where t in seconds and x in centimeter]

    Position, velocity and acceleration are all based on the equation of motion.

    The equation represents the position. The first derivative gives the velocity and the 2nd derivative gives the acceleration.

    x (t) = 8sint

    x' (t) = 8cost

    x" (t) = -8sint

    now at time t=2pi/3,

    position, x (t) = 8sin (2pi/3) = 4*squart (3) cm.

    velocity, x' (t) = 8cos (2pi/3) = =4cm/s

    acceleration, x" (t) = =8sin (2pi/3) = -4cm/s^2

    so at present the direction is in y-axis.
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