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# Trigonometric Functions

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I haven't came across a question like this in a while and I'm having quite some difficulty trying to solve it since it doesn't make much sense.

A spring modeling in a sinusoidal function rests 1.6 metres above the ground. If the mass on the spring is pulled 1.1 metres below its resting position and then released, it requires 0.5 seconds to move from the maximum position to its minimum position. Assuming friction and air resistance are neglected, write an equation in terms of cosine that describes this periodic function.

Jun 4, 2021

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They are asking you for a graph of height (of the bottom of the spring) with respect to time.

Time in seconds will be the horizontal axis, and height is the vertical axis.

The midline is the bottom of the weight when the spring is at rest. That is 1.6metres above the ground

The mass is pulled down by 1.1 metres - so that is the amplitude.

the wavelength is 1 second (1/2 +1/2)

The way I am looking at it, the spring starts at the bottom of its cycle so this is a reflection of the usual cos graph about the line y=1.6

so the equation is

y=-1.1cos[(2pi/wavelength)x]+1.6

y = -1.1cos(2pi*x)+1.6

Jun 4, 2021