Download PreAP PreCalculus Homework – Simple Harmonic Motion A weight

PreAP PreCalculus Homework – Simple Harmonic Motion
1. A weight suspended from a spring is set into oscillating motion by compressing it into a point 3 cm above its rest
position and releasing it. Determine an equation to describe the position of the weight at the time t seconds. It
takes 1.2 seconds for the weight to complete one cycle. ( y  cos t parent function)
2. A person is seated on a Ferris wheel with a radius of 110 feet that makes one rotation every 35 seconds. The
center of the wheel is 114 feet above ground. Determine and graph an equation to represent the person’s
height at anytime t of a 3 minute ride. Assume that the ride begins at the bottom of the wheel. ( y  cos t
parent function)
3. A high tide in a bay is 4 meters above sea level and a low tide is 4 meters below sea level. The time between high
tides is approximately 12 hours. Assuming that it is high tide at t  0 , determine an equation describing the
motion of the tides. ( y  cos t parent function)
4. The horizontal distance, d, of the tip of a pendulum from its vertical position at rest can be described by a
sinusoidal function. Assuming that pendulum is at rest at t  0 , maximum displacement is 12cm and one cycle is
in 2 seconds, determine an equation of the motion for the tip of the pendulum. ( y  sin t parent function)
5. The usual 110V household alternating current varies from -155 to 155V with a frequency of 60 cycles per
second. Determine an equation that describes the variation in voltage. ( y  sin t parent function)
PreAP PreCalculus Homework – Simple Harmonic Motion
1. A weight suspended from a spring is set into oscillating motion by compressing it into a point 3 cm above its rest
position and releasing it. Determine an equation to describe the position of the weight at the time t seconds. It
takes 1.2 seconds for the weight to complete one cycle. ( y  cos t parent function)
2. A person is seated on a Ferris wheel with a radius of 110 feet that makes one rotation every 35 seconds. The
center of the wheel is 114 feet above ground. Determine and graph an equation to represent the person’s
height at anytime t of a 3 minute ride. Assume that the ride begins at the bottom of the wheel. ( y  cos t
parent function)
3. A high tide in a bay is 4 meters above sea level and a low tide is 4 meters below sea level. The time between high
tides is approximately 12 hours. Assuming that it is high tide at t  0 , determine an equation describing the
motion of the tides. ( y  cos t parent function)
4. The horizontal distance, d, of the tip of a pendulum from its vertical position at rest can be described by a
sinusoidal function. Assuming that pendulum is at rest at t  0 , maximum displacement is 12cm and one cycle is
in 2 seconds, determine an equation of the motion for the tip of the pendulum. ( y  sin t parent function)
5. The usual 110V household alternating current varies from -155 to 155V with a frequency of 60 cycles per
second. Determine an equation that describes the variation in voltage. ( y  sin t parent function)