## Math Problem Statement

An object attached to a spring oscillates 12 centimeters above and b elow its equilibrium position of 25 centimeters above the table. A stopwatch was started at t = 0 to time the oscillations. The object reached its max height at t = 0.2 seconds. The object reached its lowest height 0.3 seconds after reaching it's max height.

A) Sketch a graph of the function showing one complete cycle, label the max and min valuies and the midlione. Scale the X axis to indicate the period.

B) Formulate the equation of a function of the form h(t) = a cos b(t - c) + d that represents the objects height above the table, h(t) in reltion to time t. Use the function to determine the height of the oject 3.4 secondsa fter thestopwatch started.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Trigonometry

Periodic Functions

Harmonic Motion

### Formulas

h(t) = a cos(b(t - c)) + d

Period = 2π / b

### Theorems

Cosine Function

Oscillatory Motion in Physics

### Suitable Grade Level

Grades 11-12

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