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Question

a spring models a sinusoidal function and rests 1.8 m above the ground. A mass on the spring is pulled 1m below its resting point and released, it takes 0.5 seconds to move from the minimum position to the maximum position.

Q1. how to model the function in terms of cosine?

Q2. How to find the height of the spring 3.0 seconds after being released.

Answer 1

The period P = 2 * .5 = 1

ω = 2 π / P = 2 π/1 = 2 π

The Amplitude of the cycle is 1 m

The displacement is 1.8 m

It is at a minimum at time 0; cos is a minimum at π or - π

Since ω = 2 π, this is half a cycle

Thus, the equation is 1.8 + 1 cos 2 π (t + 1/2)

At t = 3, the value is the same as at t = 0, .8