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1, In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. (d) Find the period and amplitude of the motion.2, A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.00 cm, and the frequency is 1.50 Hz. (a) Find the relation between the position of the particle and time t(b) the maximum speed and the earliest time (t 0) at which the particle has this speed, (c) the maximum acceleration in positive direction and the earliest time (t 0) at which the particle has this acceleration, and (d) the total distance traveled between t =0 and t = 1.00 s.3, A particle with a mass of 0.500 kg is attached to a spring with a force constant of 50.0 N/m. At time t = 0 the particle has its maximum speed of 20.0 m/s and is moving to the left. (a) Determine the particles equation of motion, specifying its position as a function of time.(b) Where in the motion
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