# A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position y = 1.5sin8t -...

A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position

y = 1.5sin8t - 0.5cos8t

use the identity:

asinBx + bcosBx = y = square root of (a^2 + b^2) sin(Bt + C)

to write the model in the form: y = square root of (a^2 + B^2) sin(Bt + C)

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### 1 Answer

You need to compare `y = 1.5sin8t - 0.5cos8t` to `y = asinBx + bcosBx` to identify `a=1.5, b=0.5, B=8` .

You need to substitute a=1.5, b=0.5, B=8 in the model equation `y =sqrt (a^2 + b^2) sin(Bt + C)` such that:

`y = sqrt ((1.5)^2 + (0.5)^2) sin` `(8t + C) `

**Hence, consiverting the given equation to the model equation yields `y = sqrt ((1.5)^2 + (0.5)^2) sin(8t + C).` **