Harmonic motion

1.) A mass on a spring oscillates back and forth and completes one cycle in 0.5 sec. Its maximum displacement is 3 cm. Write an equation that models this motion. Using this model, how long does it take for the weight to first reach a height of 1 cm above equilibrium? 2.) A Ferris wheel 28 ft in diameter makes one revolution every 25 sec. If the center of the wheel is 15 ft above the ground, how long after reaching the low point is the rider 21 ft above the ground? 3.) The wheel in a piston linkage (like example 1) has a radius of 6 in. It turns with an angular velocity of 16a rad/sec. The initial position is the same as example 1. a.) What is the frequency of the piston? b.) What equation models the motion of the piston? c.) What is the distance from the initial position 2.85 sec after starting? 4.) A point on the tip of a tuning fork vibrates in harmonic motion described by the equation d = 14 sin(wt). Find cu for a tuning fork that has frequency of 528 vibrations per second