A mass oscillating up and down on the bottom of a spring can be modeled as harmonic motion. if they weight is displaced a maximum of 7 cm and it takes 4.0 sec to complete one cycle to the nearest hundredth of a cm how far above or below the resting position is the weight after 1.15 seconds ?

9514 1404 393

  1.63 cm (across the centerline from release)

Step-by-step explanation:

If we assume time starts counting when we release the weight from its fully-extended downward position, then the position at 1.15 seconds can be found from ...

  h(t) = -7cos(2πt/4)

  h(1.15) = -7cos(π·1.15/2) = -7(-0.233445) ≈ 1.63412 . . . cm

That is, 1.15 seconds after the weight is released from below the resting position, it will be 1.63 cm above the resting position.

__

If it is released from above the resting position, it will be 1.63 cm below the resting position at t=1.15 seconds.