Differentiate A mass on a spring vibrates horizontally on a smooth level surface

Question

Differentiate A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Tts equation of motion is x(t) = 8 sin t, where t is in seconds and x in centimeters. Find the velocity and acceleration at time t. Find the position, velocity, and acceleration of the mass at time t = 2 pi/3. In what direction is it moving at that time? A ladder 10 ft long rests against a vertical wall. Let theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta = pi/3?

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